| \n", " | code\\ttext\\tdescription | \n", "
|---|---|
| 0 | \n", "00-XX\\t\"General and overarching topics; collections\"\\t\"General and overarching topics; collections\" | \n", "
| 1 | \n", "00Axx\\t\"General and miscellaneous specific topics\"\\t\"General and miscellaneous specific topics\" | \n", "
| 2 | \n", "00A05\\t\"Mathematics in general\"\\t\"Mathematics in general\" | \n", "
| 3 | \n", "00A08\\t\"Recreational mathematics\"\\t\"Recreational mathematics\" | \n", "
| 4 | \n", "00A09\\t\"Popularization of mathematics\"\\t\"Popularization of mathematics\" | \n", "
| \n", " | code\\ttext\\tdescription | \n", "
|---|---|
| 2 | \n", "00A05\\t\"Mathematics in general\"\\t\"Mathematics in general\" | \n", "
| 3 | \n", "00A08\\t\"Recreational mathematics\"\\t\"Recreational mathematics\" | \n", "
| 4 | \n", "00A09\\t\"Popularization of mathematics\"\\t\"Popularization of mathematics\" | \n", "
| 5 | \n", "00A15\\t\"Bibliographies for mathematics in general\"\\t\"Bibliographies for mathematics in general [See also 01A70 and the classification number --00 in the other sections]\" | \n", "
| 6 | \n", "00A17\\t\"External book reviews\"\\t\"External book reviews\" | \n", "
| ... | \n", "... | \n", "
| 3964 | \n", "97P80\\t\"Artificial intelligence (educational aspects)\"\\t\"Artificial intelligence (educational aspects)\" | \n", "
| 3966 | \n", "97U10\\t\"Comprehensive works on educational material and media and educational technology in mathematics education\"\\t\"Comprehensive works on educational material and media and educational technology in mathematics education\" | \n", "
| 3967 | \n", "97U30\\t\"Teachers' manuals and planning aids (aspects of mathematics education)\"\\t\"Teachers' manuals and planning aids (aspects of mathematics education)\" | \n", "
| 3968 | \n", "97U60\\t\"Manipulative materials (aspects of mathematics education)\"\\t\"Manipulative materials (aspects of mathematics education)\" | \n", "
| 3969 | \n", "97U80\\t\"Audiovisual media (aspects of mathematics education)\"\\t\"Audiovisual media (aspects of mathematics education)\" | \n", "
3406 rows × 1 columns
\n", "| \n", " | entry_id | \n", "updated | \n", "published | \n", "title | \n", "summary | \n", "comment | \n", "journal_ref | \n", "doi | \n", "primary_category | \n", "categories | \n", "pdf_url | \n", "authors | \n", "links | \n", "
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | \n", "http://arxiv.org/abs/2306.03752v2 | \n", "2023-06-15 17:15:27+00:00 | \n", "2023-06-06 15:10:26+00:00 | \n", "On the inviscid limit connecting Brinkman's and Darcy's models of tissue growth with nonlinear pressure | \n", "Several recent papers have addressed modelling of the tissue growth by the\\nmulti-phase models where the velocity is related to the pressure by one of the\\nphysical laws (Stoke's, Brinkman's or Darcy's). While each of these models has\\nbeen extensively studied, not so much is known about the connection between\\nthem. In the recent paper (arXiv:2303.10620), assuming the linear form of the\\npressure, the Authors connected two multi-phase models by an inviscid limit:\\nthe viscoelastic one (of Brinkman's type) and the inviscid one (of Darcy's\\ntype). Here, we prove that the same is true for a nonlinear, power-law\\npressure. The new ingredient is that we use relation between the pressure $p$\\nand the Brinkman potential $W$ to deduce compactness in space of $p$ from the\\ncompactness in space of $W$. | \n", "13 pages + appendix + bibliography; in the new version a missing\\n reference in the Appendix was added | \n", "None | \n", "None | \n", "math.AP | \n", "[math.AP, 35K45, 35K65, 35J60, 35Q92, 92C10] | \n", "http://arxiv.org/pdf/2306.03752v2 | \n", "[Charles Elbar, Jakub Skrzeczkowski] | \n", "[http://arxiv.org/abs/2306.03752v2, http://arxiv.org/pdf/2306.03752v2] | \n", "
| 1 | \n", "http://arxiv.org/abs/2306.09213v1 | \n", "2023-06-15 15:50:01+00:00 | \n", "2023-06-15 15:50:01+00:00 | \n", "Stationarity and Fredholm theory in subextremal Kerr-de Sitter spacetimes | \n", "In a recent paper, we proved that solutions to linear wave equations in a\\nsubextremal Kerr-de Sitter spacetime have asymptotic expansions in quasinormal\\nmodes up to a decay order given by the normally hyperbolic trapping, extending\\nthe existing results. One central ingredient in the argument was a new\\ndefinition of quasinormal modes, where a non-standard choice of stationary\\nKilling vector field had to be used in order for the Fredholm theory to be\\napplicable. In this paper, we show that there is in fact a variety of allowed\\nchoices of stationary Killing vector fields. In particular, the horizon Killing\\nvector fields work for the analysis, in which case one of the corresponding\\nergoregions is completely removed. | \n", "13 pages. arXiv admin note: text overlap with arXiv:2112.01355 | \n", "None | \n", "None | \n", "math.AP | \n", "[math.AP, gr-qc, math.DG, 35L05, 35P25, 58J45, 83C30] | \n", "http://arxiv.org/pdf/2306.09213v1 | \n", "[Oliver Petersen, András Vasy] | \n", "[http://arxiv.org/abs/2306.09213v1, http://arxiv.org/pdf/2306.09213v1] | \n", "
| 2 | \n", "http://arxiv.org/abs/2305.14134v2 | \n", "2023-06-15 14:55:58+00:00 | \n", "2023-05-23 14:57:51+00:00 | \n", "Remarks on paper \"Two-term spectral asymptotics in linear elasticity'' | \n", "In this note, by pointing out several serious mistakes in \\cite{CaFrLeVa-23}\\nwe show that the conclusions published by Matteo Capoferri, Leonid Friedlander,\\nMichael Levitin and Dmitri Vassiliev (J Geom Anal (2023)33:242) are completely\\nwrong. Then, we explain the correctness of proof of Theorem 1.1 in our paper\\n\\cite{Liu-21} by giving some remarks and putting the whole proof in Appendix\\n(see also \\cite{Liu-22b} and \\cite{Liu-22c}). | \n", "30 pages | \n", "None | \n", "None | \n", "math.SP | \n", "[math.SP, math-ph, math.AP, math.DG, math.MP] | \n", "http://arxiv.org/pdf/2305.14134v2 | \n", "[Genqian Liu] | \n", "[http://arxiv.org/abs/2305.14134v2, http://arxiv.org/pdf/2305.14134v2] | \n", "
| 3 | \n", "http://arxiv.org/abs/2306.09168v1 | \n", "2023-06-15 14:45:57+00:00 | \n", "2023-06-15 14:45:57+00:00 | \n", "Existence and uniqueness of weak solutions to the Smoluchowski coagulation equation with source and sedimentation | \n", "This article is devoted to a generalized version of Smoluchowski's\\ncoagulation equation. This model describes the time evolution of a system of\\naggregating particles under the effect of external input and output particles.\\nWe show that for a large class of coagulation kernels, output rates, and\\nexponentially decaying input rates, there is a weak solution. Moreover, the\\nsolution satisfies the mass-conservation property for linear coagulation rate\\nand an additional condition on input and output rates. The uniqueness of weak\\nsolutions is also established by applying additional restrictions on the rates. | \n", "20 Pages | \n", "None | \n", "None | \n", "math.AP | \n", "[math.AP] | \n", "http://arxiv.org/pdf/2306.09168v1 | \n", "[Prasanta Kumar Barik, Asha K. Dond, Rakesh Kumar] | \n", "[http://arxiv.org/abs/2306.09168v1, http://arxiv.org/pdf/2306.09168v1] | \n", "
| 4 | \n", "http://arxiv.org/abs/2306.02490v2 | \n", "2023-06-15 14:33:08+00:00 | \n", "2023-06-04 21:49:21+00:00 | \n", "A short proof of Allard's and Brakke's regularity theorems | \n", "We give new short proofs of Allard's regularity theorem for varifolds with\\nbounded first variation and Brakke's regularity theorem for integral Brakke\\nflows with bounded forcing. They are based on a decay of flatness, following\\nfrom weighted versions of the respective monotonicity formulas, together with a\\ncharacterization of non-homogeneous blow-ups using the viscosity approach\\nintroduced by Savin. | \n", "Typos corrected | \n", "None | \n", "None | \n", "math.AP | \n", "[math.AP, math.DG] | \n", "http://arxiv.org/pdf/2306.02490v2 | \n", "[Guido De Philippis, Carlo Gasparetto, Felix Schulze] | \n", "[http://arxiv.org/abs/2306.02490v2, http://arxiv.org/pdf/2306.02490v2] | \n", "
| ... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "
| 4995 | \n", "http://arxiv.org/abs/2109.09441v2 | \n", "2022-09-29 15:01:59+00:00 | \n", "2021-09-20 12:02:55+00:00 | \n", "Liouville-type theorems, radial symmetry and integral representation of solutions to Hardy-Hénon equations involving higher order fractional Laplacians | \n", "We study nonnegative solutions to the following Hardy-H\\'enon type equations\\ninvolving higher order fractional Laplacians $$ (-\\Delta)^\\sigma u =\\n|x|^{-\\alpha}u^{p} ~~~~~~ in ~~ \\mathbb{R}^n \\backslash \\{0\\} $$ which have a\\npossible singularity at the origin, where $\\sigma$ is a real number satisfying\\n$0 < \\sigma < n/2$, $-\\infty < \\alpha < 2\\sigma$ and $p>1$. By a more direct\\napproach without using the super poly-harmonic properties of nonnegative\\nsolutions, we establish an integral representation for nonnegative solutions to\\nthe above higher order fractional equations whether the singularity $\\{0\\}$ is\\nremovable or not. As the first application, we prove Liouville theorems for\\nnonnegative solutions to the above equations with removable singularity for all\\n$\\sigma \\in (0, n/2)$ when $$ 1 < p < p_{\\sigma,\\alpha}^*:=\\frac{n+2\\sigma\\n-2\\alpha}{n-2\\sigma}~~~ and ~~~ -\\infty < \\alpha < 2\\sigma. $$ This, in\\nparticular, covers a gap occurring for non-integral $\\sigma \\in (1, n/2)$ and\\n$\\alpha \\in (0, 2\\sigma)$ in the current literature. As the second application,\\nwe show the radial symmetry of nonnegative solutions to the above equations in\\nthe critical case or in the case where the singularity at the origin is not\\nremovable. Such radial symmetry would be useful in studying the higher order\\nsingular Yamabe problems and characterizing isolated singularities of the\\nhigher order Hardy-H\\'enon equations. | \n", "33 pages. Minor changes were made, and references were added | \n", "None | \n", "None | \n", "math.AP | \n", "[math.AP] | \n", "http://arxiv.org/pdf/2109.09441v2 | \n", "[Hui Yang] | \n", "[http://arxiv.org/abs/2109.09441v2, http://arxiv.org/pdf/2109.09441v2] | \n", "
| 4996 | \n", "http://arxiv.org/abs/2209.14762v1 | \n", "2022-09-29 13:18:07+00:00 | \n", "2022-09-29 13:18:07+00:00 | \n", "Long-time asymptotic estimate and a related inverse source problem for time-fractional wave equations | \n", "Lying between traditional parabolic and hyperbolic equations, time-fractional\\nwave equations of order $\\alpha\\in(1,2)$ in time inherit both decaying and\\noscillating properties. In this article, we establish a long-time asymptotic\\nestimate for homogeneous time-fractional wave equations, which readily implies\\nthe strict positivity/negativity of the solution for $t\\gg1$ under some sign\\nconditions on initial values. As a direct application, we prove the uniqueness\\nfor a related inverse source problem on determining the temporal component. | \n", "15 pages, 1 figure | \n", "None | \n", "None | \n", "math.AP | \n", "[math.AP] | \n", "http://arxiv.org/pdf/2209.14762v1 | \n", "[Xinchi Huang, Yikan Liu] | \n", "[http://arxiv.org/abs/2209.14762v1, http://arxiv.org/pdf/2209.14762v1] | \n", "
| 4997 | \n", "http://arxiv.org/abs/2209.14729v1 | \n", "2022-09-29 12:49:35+00:00 | \n", "2022-09-29 12:49:35+00:00 | \n", "Local well-posedness for the compressible Navier-Stokes-BGK model in Sobolev spaces with exponential weight | \n", "Sprays are complex flows constituted of dispersed particles in an underlying\\ngas. In this paper, we are interested in the equations for moderately thick\\nsprays consisting of the compressible Navier-Stokes equations and Boltzmann BGK\\nequation. Here the coupling of two equations is through a friction (or drag)\\nforce which depends on the density of compressible fluid and the relative\\nvelocity between particles and fluid. For the Navier-Stokes-BGK system, we\\nestablish the existence and uniqueness of solutions in Sobolev spaces with\\nexponential weight. | \n", "None | \n", "None | \n", "None | \n", "math.AP | \n", "[math.AP] | \n", "http://arxiv.org/pdf/2209.14729v1 | \n", "[Young-Pil Choi, Jinwook Jung] | \n", "[http://arxiv.org/abs/2209.14729v1, http://arxiv.org/pdf/2209.14729v1] | \n", "
| 4998 | \n", "http://arxiv.org/abs/2209.14706v1 | \n", "2022-09-29 12:07:20+00:00 | \n", "2022-09-29 12:07:20+00:00 | \n", "Iterative Approach to Image Compression with Noise : Optimizing Spatial and Tonal Data | \n", "We consider some iterative methods for finding the best interpolation data in\\nthe images compression with noise. The interpolation data consists of the set\\nof pixels and their grey/color values. The aim in the iterative approach is to\\nallow the change of the data dynamically during the inpainting process for a\\nreconstruction of the image that includes the enhancement and denoising\\neffects. The governing PDE model of this approach is a fully parabolic problem\\nwhere the set of stored pixels is time dependent. We consider the semi-discrete\\ndynamical system associated to the model which gives rise to an iterative\\nmethod where the stored data are modified during the iterations for best\\noutcomes. Finding the compression sets follows from a shape-based analysis\\nwithin the $\\Gamma$-convergence tools, in particular well suited topological\\nasymptotic and a ``fat pixels'' approach are considered to obtain an analytic\\ncharacterization of the optimal sets in the sense of shape optimization theory.\\nWe perform the analysis and derive several iterative algorithms that we\\nimplement and compare to obtain the most efficient strategies of compression\\nand inpainting for noisy images. Some numerical computations are presented to\\nconfirm the theoretical findings. Finally, we propose a modified model that\\nallows the inpainting data to change with the iteration and compare the\\nresulting new method to the ``probabilistic'' ones from the state-of-the-art. | \n", "arXiv admin note: text overlap with arXiv:2202.10702 | \n", "None | \n", "None | \n", "math.AP | \n", "[math.AP] | \n", "http://arxiv.org/pdf/2209.14706v1 | \n", "[Zakaria Belhachmi, Thomas Jacumin] | \n", "[http://arxiv.org/abs/2209.14706v1, http://arxiv.org/pdf/2209.14706v1] | \n", "
| 4999 | \n", "http://arxiv.org/abs/2012.13879v2 | \n", "2022-09-29 10:50:59+00:00 | \n", "2020-12-27 06:54:57+00:00 | \n", "Blowup dynamics for smooth equivariant solutions to energy critical Landau-Lifschitz flow | \n", "In this paper, we study the energy critical 1-equivariant Landau-Lifschitz\\nflow mapping $\\mathbb{R}^2$ to $\\mathbb{S}^2$ with arbitrary given coefficients\\n$\\rho_1\\in \\mathbb{R}$, $\\rho_2>0$. We prove that there exists a codimension\\none smooth well-localized set of initial data arbitrarily close to the ground\\nstate which generates type-II finite-time blowup solutions, and give a precise\\ndescription of the corresponding singularity formation. In our proof, both the\\nSchr\\\"odinger part and the heat part play important roles in the construction\\nof approximate solutions and the mixed energy/Morawetz functional. However, the\\nblowup rate is independent of the coefficients. | \n", "84 pages | \n", "None | \n", "None | \n", "math.AP | \n", "[math.AP] | \n", "http://arxiv.org/pdf/2012.13879v2 | \n", "[Jitao Xu, Lifeng Zhao] | \n", "[http://arxiv.org/abs/2012.13879v2, http://arxiv.org/pdf/2012.13879v2] | \n", "
5000 rows × 13 columns
\n", "| \n", " | title | \n", "summary | \n", "authors | \n", "primary_category | \n", "categories | \n", "hyph_in_summary | \n", "hyph_in_title | \n", "msc_tags | \n", "
|---|---|---|---|---|---|---|---|---|
| 4996 | \n", "Long-time asymptotic estimate and a related inverse source problem for time-fractional wave equations | \n", "Lying between traditional parabolic and hyperbolic equations, time-fractional wave equations of order LATEX in time inherit both decaying and oscillating properties. In this article, we establish a long-time asymptotic estimate for homogeneous time-fractional wave equations, which readily implies the strict positivity/negativity of the solution for LATEX under some sign conditions on initial values. As a direct application, we prove the uniqueness for a related inverse source problem on determining the temporal component. | \n", "[Xinchi Huang, Yikan Liu] | \n", "math.AP | \n", "[math.AP] | \n", "[long-time, time-fractional] | \n", "[time-fractional, Long-time] | \n", "None | \n", "
| 1412 | \n", "Convergence rates in the nonrelativistic limit of the cubic Klein-Gordon equation | \n", "In this paper, we study the nonrelativistic limit of the cubic nonlinear Klein-Gordon equation in LATEX with a small parameter LATEX which is inversely proportional to the speed of light. We show that the cubic nonlinear Klein-Gordon equation converges to the cubic nonlinear Schrodinger equation with a convergence rate of order LATEX In particular, for the defocusing case and smooth initial data, we prove error estimates of the form LATEX at time LATEX which is valid up to long time of order LATEX while for nonsmooth initial data, we prove error estimates of the form LATEX at time LATEX which is valid up to long time of order LATEX These specific forms of error estimates coincide with the numerical results obtained in . | \n", "[Weizhu Bao, Yong Lu, Zhifei Zhang] | \n", "math.AP | \n", "[math.AP] | \n", "[Klein-Gordon] | \n", "[Klein-Gordon] | \n", "None | \n", "
| 3812 | \n", "On potential theory of Markov processes with jump kernels decaying at the boundary | \n", "Motivated by some recent potential theoretic results on subordinate killed Levy processes in open subsets of the Euclidean space, we study processes in an open set LATEX defined via Dirichlet forms with jump kernels of the form LATEX and critical killing functions. Here LATEX is the Levy density of an isotropic stable process (or more generally, a pure jump isotropic unimodal Levy process) in LATEX The main novelty is that the term LATEX tends to 0 when LATEX or LATEX approach the boundary of LATEX Under some general assumptions on LATEX we construct the corresponding process and prove that non-negative harmonic functions of the process satisfy the Harnack inequality and Carleson's estimate. We give several examples of boundary terms satisfying those assumptions. The examples depend on four parameters, LATEX LATEX roughly governing the decay of the boundary term near the boundary of LATEX In the second part of this paper, we specialise to the case of the half-space LATEX the LATEX kernel LATEX and the killing function$appa(x)=c x_d^{-\\alpha}$, LATEX where LATEX is a positive constant. Our main result in this part is a boundary Harnack principle which says that, for any LATEX there are values of the parameters LATEX LATEX and the constant LATEX such that non-negative harmonic functions of the process must decay at the rate LATEX if they vanish near a portion of the boundary. We further show that there are values of the parameters LATEX LATEX for which the boundary Harnack principle fails despite the fact that Carleson's estimate is valid. | \n", "[Panki Kim, Renming Song, Zoran Vondraček] | \n", "math.PR | \n", "[math.PR, math.AP, math.FA, 60J45, 60J50, 60J75] | \n", "[half-space, non-negative] | \n", "None | \n", "[Boundary theory for Markov processes] | \n", "
| 3040 | \n", "Fractional Zernike functions | \n", "We consider and provide an accurate study for the fractional Zernike functions on the punctured unit disc, generalizing the classical Zernike polynomials and their associated LATEX Zernike functions. Mainly, we give the spectral realization of the latter ones and show that they are orthogonal LATEX for certain perturbed magnetic (hyperbolic) Laplacian. The algebraic and analytic properties for the fractional Zernike functions to be established include the connection to special functions, their zeros, their orthogonality property, as well as the differential equations, recurrence, and operational formulas they satisfy. Integral representations are also obtained. Their regularity as poly-meromorphic functions is discussed and their generating functions including a bilinear one of \"Hardy--Hille type\" are derived. Moreover, we prove that a truncated subclass defines a complete orthogonal system in the underlying Hilbert space giving rise to a specific Hilbertian orthogonal decomposition in terms of a second class of generalized Bergman spaces. | \n", "[Hajar Dkhissi, Allal Ghanmi, Safa Snoun] | \n", "math.CV | \n", "[math.CV, math.AP] | \n", "[poly-meromorphic] | \n", "None | \n", "None | \n", "
| 4377 | \n", "The Isochronal Phase of Stochastic PDE and Integral Equations: Metastability and Other Properties | \n", "We study the dynamics of waves, oscillations, and other spatio-temporal patterns in stochastic evolution systems, including SPDE and stochastic integral equations. Representing a given pattern as a smooth, stable invariant manifold of the deterministic dynamics, we reduce the stochastic dynamics to a finite dimensional SDE on this manifold using the isochronal phase. The isochronal phase is defined by mapping a neighbourbhood of the manifold onto the manifold itself, analogous to the isochronal phase defined for finite-dimensional oscillators by A.T.~Winfree and J.~Guckenheimer. We then determine a probability measure that indicates the average position of the stochastic perturbation of the pattern/wave as it wanders over the manifold. It is proved that this probability measure is accurate on time-scales greater than LATEX but less than LATEX where LATEX is the amplitude of the stochastic perturbation. Moreover, using this measure, we determine the expected velocity of the difference between the deterministic and stochastic motion on the manifold. | \n", "[Zachary P. Adams, James MacLaurin] | \n", "math.PR | \n", "[math.PR, math.AP, 60H15, 35R60] | \n", "[finite-dimensional, spatio-temporal, time-scales] | \n", "None | \n", "[Stochastic partial differential equations (aspects of stochastic analysis)] | \n", "
| 2527 | \n", "Multiscale modelling and analysis of growth of plant tissues | \n", "How morphogenesis depends on cell properties is an active direction of research. Here, we focus on mechanical models of growing plant tissues, where microscopic (sub)cellular structure is taken into account. In order to establish links between microscopic and macroscopic tissue properties, we perform a multiscale analysis of a model of growing plant tissue with subcellular resolution. We use homogenization to rigorously derive the corresponding macroscopic tissue scale model. Tissue scale mechanical properties are computed from all microscopic structural and material properties, taking into account deformation by the growth field. We then consider case studies and numerically compare the detailed microscopic model and the tissue-scale model, both implemented using finite element method. We find that the macroscopic model can be used to efficiently make predictions about several configurations of interest. Our work will help making links between microscopic measurements and macroscopic observations in growing tissues. | \n", "[Arezki Boudaoud, Annamaria Kiss, Mariya Ptashnyk] | \n", "math.AP | \n", "[math.AP, q-bio.TO, 35B27, 74S05, 74Qxx, 92C80, 65M60] | \n", "[tissue-scale] | \n", "None | \n", "[Finite element methods applied to problems in solid mechanics] | \n", "
| 829 | \n", "An elementary proof of existence and uniqueness for the Euler flow in localized Yudovich spaces | \n", "We revisit Yudovich's well-posedness result for the LATEX Euler equations for an inviscid incompressible fluid on either a sufficiently regular (not necessarily bounded) open set LATEX or on the torus LATEX We construct global-in-time weak solutions with vorticity in LATEX and in LATEX where LATEX and LATEX are suitable uniformly-localized versions of the Lebesgue space LATEX and of the Yudovich space LATEX respectively, with no condition at infinity for the growth function LATEX We also provide an explicit modulus of continuity for the velocity depending on the growth function LATEX We prove uniqueness of weak solutions in LATEX under the assumption that LATEX grows moderately at infinity. In contrast to Yudovich's energy method, we employ a Lagrangian strategy to show uniqueness. Our entire argument relies on elementary real-variable techniques, with no use of either Sobolev spaces, Calderon-Zygmund theory or Littlewood-Paley decomposition, and actually applies not only to the Biot-Savart law, but also to more general operators whose kernels obey some natural structural assumptions. | \n", "[Gianluca Crippa, Giorgio Stefani] | \n", "math.AP | \n", "[math.AP, Primary 76B03. Secondary 35Q35] | \n", "[Biot-Savart, Littlewood-Paley, Calderon-Zygmund, global-in-time, well-posedness, uniformly-localized, real-variable] | \n", "None | \n", "[PDEs in connection with fluid mechanics] | \n", "
| 3471 | \n", "Hamiltonian Birkhoff normal form for gravity-capillary water waves with constant vorticity: almost global existence | \n", "We prove an almost global in time existence result of small amplitude space periodic solutions of the 1D gravity-capillary water waves equations with constant vorticity. The result holds for any value of gravity, vorticity and depth and any surface tension belonging to a full measure set. The proof demands a Hamiltonian paradifferential Birkhoff normal form reduction for quasi-linear PDEs in presence of resonant wave interactions: the normal form may be not integrable but it preserves the Sobolev norms thanks to its Hamiltonian nature. A major difficulty is that usual paradifferential calculus used to prove local well posedness (as the celebrated Alinhac good unknown) does not preserve the Hamiltonian structure. A major novelty of this paper is to develop an algorithmic perturbative procedure a la Darboux to correct usual paradifferential transformations to symplectic maps, up to an arbitrary degree of homogeneity. The symplectic correctors turn out to be smoothing perturbations of the identity, and therefore only slightly modify the paradifferential structure of the equations. The Darboux procedure which recovers the nonlinear Hamiltonian structure is written in an abstract functional setting, in order to be applicable also in other contexts. | \n", "[Massimiliano Berti, Alberto Maspero, Federico Murgante] | \n", "math.AP | \n", "[math.AP] | \n", "[gravity-capillary, quasi-linear] | \n", "[gravity-capillary] | \n", "None | \n", "
| 4239 | \n", "Taylor dispersion and phase mixing in the non-cutoff Boltzmann equation on the whole space | \n", "In this paper, we describe the long-time behavior of the non-cutoff Boltzmann equation with soft potentials near a global Maxwellian background on the whole space in the weakly collisional limit (i.e. infinite Knudsen number LATEX Specifically, we prove that for initial data sufficiently small (independent of the Knudsen number), the solution displays several dynamics caused by the phase mixing/dispersive effects of the transport operator LATEX and its interplay with the singular collision operator. For LATEX LATEX with LATEX one sees an enhanced dissipation effect wherein the characteristic decay time-scale is accelerated to LATEX where LATEX is the singularity of the kernel ($s=1$ being the Landau collision operator, which is also included in our analysis); for LATEX one sees Taylor dispersion, wherein the decay is accelerated to LATEX Additionally, we prove almost-uniform phase mixing estimates. For macroscopic quantities as the density LATEX these bounds imply almost-uniform-in-$\\nu$ decay of LATEX in LATEX due to Landau damping and dispersive decay. | \n", "[Jacob Bedrossian, Michele Coti Zelati, Michele Dolce] | \n", "math.AP | \n", "[math.AP, math-ph, math.MP, 35Q20] | \n", "[non-cutoff, long-time, almost-uniform, time-scale] | \n", "[non-cutoff] | \n", "None | \n", "
| 2509 | \n", "Weighted Lorentz-Sobolev estimates for fully nonlinear elliptic equations under relaxed convexity assumptions with oblique boundary conditions | \n", "In this work, we develop weighted Lorentz-Sobolev estimates for viscosity solutions of fully nonlinear elliptic equations under weakened convexity conditions and with oblique derivative boundary conditions under suitable assumptions about the data. Furthermore, we obtain Lorentz-Sobolev estimates for solutions to the obstacle problem and other important applications. | \n", "[Junior da S. Bessa, Gleydson C. Ricarte] | \n", "math.AP | \n", "[math.AP] | \n", "[Lorentz-Sobolev] | \n", "[Lorentz-Sobolev] | \n", "None | \n", "
| \n", " | title | \n", "summary | \n", "authors | \n", "primary_category | \n", "categories | \n", "hyph_in_summary | \n", "hyph_in_title | \n", "msc_tags | \n", "
|---|---|---|---|---|---|---|---|---|
| 0 | \n", "The Laplace spectrum on conformally compact ma... | \n", "We consider the spectrum of the Laplace operat... | \n", "[Nelia Charalambous, Julie Rowlett] | \n", "math.SP | \n", "[math.SP, 58c40] | \n", "None | \n", "None | \n", "None | \n", "
| 1 | \n", "On the inviscid limit connecting Brinkman's an... | \n", "Several recent papers have addressed modelling... | \n", "[Charles Elbar, Jakub Skrzeczkowski] | \n", "math.AP | \n", "[math.AP, 35K45, 35K65, 35J60, 35Q92, 92C10] | \n", "[power-law, multi-phase] | \n", "None | \n", "[Initial value problems for second-order parab... | \n", "
| 2 | \n", "A sparse approximation of the Lieb functional ... | \n", "The aim of this paper is to present new sparsi... | \n", "[Virginie Ehrlacher, Luca Nenna] | \n", "math-ph | \n", "[math-ph, math.MP, math.OC, math.SP] | \n", "[so-called, anti-symmetric, Levy-Lieb, trace-c... | \n", "None | \n", "None | \n", "
| 3 | \n", "Stationarity and Fredholm theory in subextrema... | \n", "In a recent paper, we proved that solutions to... | \n", "[Oliver Petersen, András Vasy] | \n", "math.AP | \n", "[math.AP, gr-qc, math.DG, 35L05, 35P25, 58J45,... | \n", "[non-standard, Kerr-de] | \n", "[Kerr-de] | \n", "[Wave equation] | \n", "
| 4 | \n", "Remarks on paper \"Two-term spectral asymptotic... | \n", "In this note, by pointing out several serious ... | \n", "[Genqian Liu] | \n", "math.SP | \n", "[math.SP, math-ph, math.AP, math.DG, math.MP] | \n", "None | \n", "[Two-term] | \n", "None | \n", "
| \n", " | clean_title | \n", "clean_abstract | \n", "authors | \n", "msc_tags | \n", "msc_cos_sim | \n", "
|---|---|---|---|---|---|
| 0 | \n", "The Laplace spectrum on conformally compact manifolds | \n", "We consider the spectrum of the Laplace operator acting on LATEX over a conformally compact manifold for LATEX We prove that for LATEX this spectrum always contains an open region of the complex plane. We further show that the spectrum is contained within a certain parabolic region of the complex plane. These regions depend on the value of LATEX the dimension of the manifold, and the values of the sectional curvatures approaching the boundary. | \n", "[Nelia Charalambous, Julie Rowlett] | \n", "None | \n", "NaN | \n", "
| 1 | \n", "On the inviscid limit connecting Brinkman's and Darcy's models of tissue growth with nonlinear pressure | \n", "Several recent papers have addressed modelling of the tissue growth by the multi-phase models where the velocity is related to the pressure by one of the physical laws (Stoke's, Brinkman's or Darcy's). While each of these models has been extensively studied, not so much is known about the connection between them. In the recent paper (arXiv:2303.10620), assuming the linear form of the pressure, the Authors connected two multi-phase models by an inviscid limit: the viscoelastic one (of Brinkman's type) and the inviscid one (of Darcy's type). Here, we prove that the same is true for a nonlinear, power-law pressure. The new ingredient is that we use relation between the pressure LATEX and the Brinkman potential LATEX to deduce compactness in space of LATEX from the compactness in space of LATEX | \n", "[Charles Elbar, Jakub Skrzeczkowski] | \n", "[Initial value problems for second-order parabolic systems, Degenerate parabolic equations, Nonlinear elliptic equations, Biomechanics] | \n", "NaN | \n", "
| 2 | \n", "A sparse approximation of the Lieb functional with moment constraints | \n", "The aim of this paper is to present new sparsity results about the so-called Lieb functional, which is a key quantity in Density Functional Theory for electronic structure calculations for molecules. The Lieb functional was actually shown by Lieb to be a convexification of the so-called Levy-Lieb functional. Given an electronic density for a system of LATEX electrons, which may be seen as a probability density on LATEX the value of the Lieb functional for this density is defined as the solution of a quantum multi-marginal optimal transport problem, which reads as a minimization problem defined on the set of trace-class operators acting on the space of electronic wave-functions that are anti-symmetric LATEX functions of LATEX with partial trace equal to the prescribed electronic density. We introduce a relaxation of this quantum optimal transport problem where the full partial trace constraint is replaced by a finite number of moment constraints on the partial trace of the set of operators. We show that, under mild assumptions on the electronic density, there exist sparse minimizers to the resulting moment constrained approximation of the Lieb (MCAL) functional that read as operators with rank at most equal to the number of moment constraints. We also prove under appropriate assumptions on the set of moment functions that the value of the MCAL functional converges to the value of the exact Lieb functional as the number of moments go to infinity. We also prove some rates of convergence on the associated approximation of the ground state energy. We finally study the mathematical properties of the associated dual problem. | \n", "[Virginie Ehrlacher, Luca Nenna] | \n", "None | \n", "NaN | \n", "
| 3 | \n", "Stationarity and Fredholm theory in subextremal Kerr-de Sitter spacetimes | \n", "In a recent paper, we proved that solutions to linear wave equations in a subextremal Kerr-de Sitter spacetime have asymptotic expansions in quasinormal modes up to a decay order given by the normally hyperbolic trapping, extending the existing results. One central ingredient in the argument was a new definition of quasinormal modes, where a non-standard choice of stationary Killing vector field had to be used in order for the Fredholm theory to be applicable. In this paper, we show that there is in fact a variety of allowed choices of stationary Killing vector fields. In particular, the horizon Killing vector fields work for the analysis, in which case one of the corresponding ergoregions is completely removed. | \n", "[Oliver Petersen, András Vasy] | \n", "[Wave equation, Scattering theory for PDEs, Hyperbolic equations on manifolds] | \n", "NaN | \n", "
| 4 | \n", "Remarks on paper \"Two-term spectral asymptotics in linear elasticity'' | \n", "In this note, by pointing out several serious mistakes in we show that the conclusions published by Matteo Capoferri, Leonid Friedlander, Michael Levitin and Dmitri Vassiliev (J Geom Anal (2023)33:242) are completely wrong. Then, we explain the correctness of proof of Theorem 1.1 in our paper by giving some remarks and putting the whole proof in Appendix (see also and ). | \n", "[Genqian Liu] | \n", "None | \n", "NaN | \n", "
| \n", " | title | \n", "summary | \n", "categories | \n", "id | \n", "
|---|---|---|---|---|
| 0 | \n", "Boundedness, Ultracontractive Bounds and Optim... | \n", "We investigate some regularity properties of a... | \n", "[math.AP, 35B65, 35D30, 35K10, 35B45] | \n", "2306.17152v1 | \n", "
| 1 | \n", "The compressible Navier-Stokes equations with ... | \n", "We show the global existence of a weak solutio... | \n", "[math.AP, 35Q30, 76D03, 35K85] | \n", "2305.00822v2 | \n", "
| 2 | \n", "A simple reaction-diffusion system as a possib... | \n", "Chemotaxis is a directed cell movement in resp... | \n", "[math.AP, 92-10] | \n", "2211.06933v3 | \n", "
| 3 | \n", "Optimal blowup stability for three-dimensional... | \n", "We study corotational wave maps from $(1+3)$-d... | \n", "[math.AP, math-ph, math.MP] | \n", "2212.08374v3 | \n", "
| 4 | \n", "A Note on $L^1-$contractive property of the so... | \n", "In this note, we study the $L^1-$contractive p... | \n", "[math.AP] | \n", "2306.17064v1 | \n", "
| ... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "
| 19995 | \n", "Exact controllability of the linear Zakharov-K... | \n", "We consider the linear Zakharov-Kuznetsov equa... | \n", "[math.AP] | \n", "1912.03066v1 | \n", "
| 19996 | \n", "Blow-up for the pointwise NLS in dimension two... | \n", "We consider the Schr\\\"odinger equation in dime... | \n", "[math.AP, math-ph, math.FA, math.MP] | \n", "1808.10343v4 | \n", "
| 19997 | \n", "Inverse problems with partial data for ellipti... | \n", "For a second order formally symmetric elliptic... | \n", "[math.AP, math-ph, math.MP] | \n", "1912.03047v1 | \n", "
| 19998 | \n", "Inverse problems for the nonlinear modified tr... | \n", "This article is devoted to inverse problems fo... | \n", "[math.AP] | \n", "1912.02996v1 | \n", "
| 19999 | \n", "A non-autonomous bifurcation problem for a non... | \n", "In this paper we study the asymptotic behavior... | \n", "[math.AP] | \n", "1912.02995v1 | \n", "
20000 rows × 4 columns
\n", "