pinecone/core-2020-05-10-deduplication huggingface dataset:
Effect of acute and repeated administration of paracetamol on opioidergic and serotonergic systems in rats.

Objective and design: We investigated the antinociceptiveeffect of paracetamol or morphine after repeatedadministration and the changes in the characteristics of centralμ-, κ- and 5-HT2 receptors.Treatment: Male rats were injected twice a day for sevendays with paracetamol (400 mg/kg, i. p.) or morphine (5 mg/kg, s. c.).Methods: The antinociceptive effect was evaluated 30 minafter single and multiple doses of paracetamol and morphinethrough the hot-plate test. Binding techniques were used toevaluate the receptor characteristics in the frontal cortex.Results: Both paracetamol and morphine induced an antinociceptiveeffect on day 1 but only paracetamol maintainedthis effect for seven days while morphine did not.The number of μ-opioid receptors decreased on days 1, 3,and 7 by a similar percentage after paracetamol administration(by 29, 31 and 34 %, respectively), while morphineproduced a progressive decrease in comparison with controls(by 37, 49 and 60 %, respectively) and κ-opioid receptorswere unaffected. Both drugs similarly decreased the 5-HT2receptor number on all days of treatment (by about 30 %).Conclusions: The opioidergic and serotonergic systems areinvolved in different ways in the induction and maintenanceof antinociception after paracetamol or morphine treatment
Incompressible viscous fluid flows in a thin spherical shell

Linearized stability of incompressible viscous fluid flows in a thin
spherical shell is studied by using the two-dimensional Navier--Stokes
equations on a sphere. The stationary flow on the sphere has two singularities
(a sink and a source) at the North and South poles of the sphere. We prove
analytically for the linearized Navier--Stokes equations that the stationary
flow is asymptotically stable. When the spherical layer is truncated between
two symmetrical rings, we study eigenvalues of the linearized equations
numerically by using power series solutions and show that the stationary flow
remains asymptotically stable for all Reynolds numbers.Comment: 28 pages, 10 figure
On Kato's method for Navier--Stokes Equations

We investigate Kato's method for parabolic equations with a quadratic
non-linearity in an abstract form. We extract several properties known from
linear systems theory which turn out to be the essential ingredients for the
method. We give necessary and sufficient conditions for these conditions and
provide new and more general proofs, based on real interpolation. In
application to the Navier-Stokes equations, our approach unifies several
results known in the literature, partly with different proofs. Moreover, we
establish new existence and uniqueness results for rough initial data on
arbitrary domains in ${\mathbb R}^3$ and irregular domains in ${\mathbb R}^n$.Comment: Revised version, to appear in Journal of Mathematical Fluid
  Mechanics. New section on solutions in Morrey-spaces added. 35 page
On recurrence and ergodicity for geodesic flows on noncompact periodic
  polygonal surfaces

We study the recurrence and ergodicity for the billiard on noncompact
polygonal surfaces with a free, cocompact action of $\Z$ or $\Z^2$. In the
$\Z$-periodic case, we establish criteria for recurrence. In the more difficult
$\Z^2$-periodic case, we establish some general results. For a particular
family of $\Z^2$-periodic polygonal surfaces, known in the physics literature
as the wind-tree model, assuming certain restrictions of geometric nature, we
obtain the ergodic decomposition of directional billiard dynamics for a dense,
countable set of directions. This is a consequence of our results on the
ergodicity of $\ZZ$-valued cocycles over irrational rotations.Comment: 48 pages, 12 figure
Global existence for the generalized two-component Hunter-Saxton system

We study the global existence of solutions to a two-component generalized
Hunter-Saxton system in the periodic setting. We first prove a persistence
result of the solutions. Then for some particular choices of parameters
$(\alpha, \kappa)$, we show the precise blow-up scenarios and the existence of
global solutions to the generalized Hunter-Saxton system under proper
assumptions on the initial data. This significantly improves recent results
obtained in [M. Wunsch, DCDS Ser. B 12 (2009), 647-656] and [M. Wunsch, SIAM J.
Math. Anal. 42 (2010), 1286-1304].Comment: 22 pages; submitted in modified form on August 7, 201
On the particle paths and the stagnation points in small-amplitude
  deep-water waves

In order to obtain quite precise information about the shape of the particle
paths below small-amplitude gravity waves travelling on irrotational deep
water, analytic solutions of the nonlinear differential equation system
describing the particle motion are provided. All these solutions are not closed
curves. Some particle trajectories are peakon-like, others can be expressed
with the aid of the Jacobi elliptic functions or with the aid of the
hyperelliptic functions. Remarks on the stagnation points of the
small-amplitude irrotational deep-water waves are also made.Comment: to appear in J. Math. Fluid Mech. arXiv admin note: text overlap with
  arXiv:1106.382
New conserved vorticity integrals for moving surfaces in
  multi-dimensional fluid flow

For inviscid fluid flow in any n-dimensional Riemannian manifold, new
conserved vorticity integrals generalizing helicity, enstrophy, and entropy
circulation are derived for lower-dimensional surfaces that move along fluid
streamlines. Conditions are determined for which the integrals yield constants
of motion for the fluid. In the case when an inviscid fluid is isentropic,
these new constants of motion generalize Kelvin's circulation theorem from
closed loops to closed surfaces of any dimension.Comment: 14 pages; typos correcte
On the inviscid limit for the compressible Navier-Stokes system in an
  impermeable bounded domain

In this paper we investigate the issue of the inviscid limit for the
compressible Navier-Stokes system in an impermeable fixed bounded domain. We
consider two kinds of boundary conditions. The first one is the no-slip
condition. In this case we extend the famous conditional result obtained by
Kato in the homogeneous incompressible case. Kato proved that if the energy
dissipation rate of the viscous flow in a boundary layer of width proportional
to the viscosity vanishes then the solutions of the incompressible
Navier-Stokes equations converge to some solutions of the incompressible Euler
equations in the energy space. We provide here a natural extension of this
result to the compressible case. The other case is the Navier condition which
encodes that the fluid slips with some friction on the boundary. In this case
we show that the convergence to the Euler equations holds true in the energy
space, as least when the friction is not too large. In both cases we use in a
crucial way some relative energy estimates proved recently by Feireisl, Ja Jin
and Novotn{\'y}
A global existence result for a zero Mach number system

This paper is to study global-in-time existence of weak solutions to zero
Mach number system which derives from the full Navier-Stokes system, under a
special relationship between the viscosity coefficient and the heat
conductivity coefficient such that, roughly speaking, the source term in the
equation for the newly introduced divergence-free velocity vector field
vanishes. In dimension two, thanks to a local-in-time existence result of a
unique strong solution in critical Besov spaces given in \cite{Danchin-Liao},
for arbitrary large initial data, we will show that this unique strong solution
exists globally in time, by a weak-strong uniqueness argument
Topography influence on the Lake equations in bounded domains

We investigate the influence of the topography on the lake equations which
describe the two-dimensional horizontal velocity of a three-dimensional
incompressible flow. We show that the lake equations are structurally stable
under Hausdorff approximations of the fluid domain and $L^p$ perturbations of
the depth. As a byproduct, we obtain the existence of a weak solution to the
lake equations in the case of singular domains and rough bottoms. Our result
thus extends earlier works by Bresch and M\'etivier treating the lake equations
with a fixed topography and by G\'erard-Varet and Lacave treating the Euler
equations in singular domains
On flows of viscoelastic fluids of oldroyd type with wall slip

We consider the boundary-value problem for the steady isothermal flow of an incompressible viscoelastic liquid of
Oldroyd type in a bounded domain with a Navier type slip boundary condition. We prove that under some restrictions on
the material constants and the data, there exists a strong solution which is locally unique. The proof is based on a fixed
point argument in which the boundary-value problem is decomposed into a transport equation and a Stokes system.http://link.springer.com/journal/21hb201
Maximal dissipation and well-posedness for the compressible Euler system

We discuss the problem of well-posedness of the compressible (barotropic)
Euler system in the framework of weak solutions. The principle of maximal
dissipation introduced by C.M. Dafermos is adapted and combined with the
concept of admissible weak solutions. We use the method of convex integration
in the spirit of the recent work of C.DeLellis and L.Szekelyhidi to show
various counterexamples to well-posedness. On the other hand, we conjecture
that the principle of maximal dissipation should be retained as a possible
criterion of uniqueness as it is violated by the oscillatory solutions obtained
in the process of convex integration
An incompressible 2D didactic model with singularity and explicit
  solutions of the 2D Boussinesq equations

We give an example of a well posed, finite energy, 2D incompressible active
scalar equation with the same scaling as the surface quasi-geostrophic equation
and prove that it can produce finite time singularities. In spite of its
simplicity, this seems to be the first such example. Further, we construct
explicit solutions of the 2D Boussinesq equations whose gradients grow
exponentially in time for all time. In addition, we introduce a variant of the
2D Boussinesq equations which is perhaps a more faithful companion of the 3D
axisymmetric Euler equations than the usual 2D Boussinesq equations.Comment: 9 pages; simplified a solution formula in section 4 and added a
  sentence on the time growth rate in the solutio
Maximal regularity of the time-periodic Navier-Stokes system

Time-periodic solutions to the linearized Navier-Stokes system in the
$n$-dimensional whole-space are investigated. For time-periodic data in
$L^q$-spaces, maximal regularity and corresponding a priori estimates for the
associated time-periodic solutions are established. More specifically, a Banach
space of time-periodic vector fields is identified with the property that the
linearized Navier-Stokes operator maps this space homeomorphically onto the
$L^q$-space of time-periodic data.Comment: 19 page
Noise prevents infinite stretching of the passive field in a stochastic
  vector advection equation

A linear stochastic vector advection equation is considered; the equation may
model a passive magnetic field in a random fluid. When the driving velocity
field is rough but deterministic, in particular just H\"{o}lder continuous and
bounded, one can construct examples of infinite stretching of the passive
field, arising from smooth initial conditions. The purpose of the paper is to
prove that infinite stretching is prevented if the driving velocity field
contains in addition a white noise component.Comment: 23 pages, 4 figure
Singular limits of Voigt models in fluid dynamics

We investigate the long-term behavior, as a certain regularization parameter
vanishes, of the three-dimensional Navier-Stokes-Voigt model of a viscoelastic
incompressible fluid. We prove the existence of global and exponential
attractors of optimal regularity. We then derive explicit upper bounds for the
dimension of these attractors in terms of the three-dimensional Grashof number
and the regularization parameter. Finally, we also prove convergence of the
(strong) global attractor of the 3D Navier-Stokes-Voigt model to the (weak)
global attractor of the 3D Navier-Stokes equation. Our analysis improves and
extends recent results obtained by Kalantarov and Titi in [31].Comment: v2: the statement and proof of Theorem 5.2 have changed. In the
  previous version, the proof was based on Theorem 4.9 in a book of
  Ladyzhenskaya, which turns out to be based on a faulty assumption. See Remark
  5.5 for detail
Existence theory for stochastic power law fluids

We consider the equations of motion for an incompressible Non-Newtonian fluid
in a bounded Lipschitz domain $G\subset\mathbb R^d$ during the time intervall
$(0,T)$ together with a stochastic perturbation driven by a Brownian motion
$W$. The balance of momentum reads as $$dv=\mathrm{div}\, S\,dt-(\nabla
v)v\,dt+\nabla\pi \,dt+f\,dt+\Phi(v)\,dW_t,$$ where $v$ is the velocity, $\pi$
the pressure and $f$ an external volume force. We assume the common power law
model $S(\varepsilon(v))=\big(1+|\varepsilon(v)|\big)^{p-2} \varepsilon(v)$ and
show the existence of weak (martingale) solutions provided
$p>\tfrac{2d+2}{d+2}$. Our approach is based on the $L^\infty$-truncation and a
harmonic pressure decomposition which are adapted to the stochastic setting
Infinite energy solutions for Dissipative Euler equations in R^2

We study the Euler equations with the so-called Ekman damping in the whole 2D
space. The global well-posedness and dissipativity for the weak infinite energy
solutions of this problem in the uniformly local spaces is verified based on
the further development of the weighted energy theory for the Navier-Stokes and
Euler type problems. In addition, the existence of weak locally compact global
attractor is proved and some extra compactness of this attractor is obtained.Comment: arXiv admin note: text overlap with arXiv:1203.573
Degenerate pullback attractors for the 3D Navier-Stokes equations

As in our previous paper, the 3D Navier-Stokes equations with a
translationally bounded force contain pullback attractors in a weak sense.
Moreover, those attractors consist of complete bounded trajectories. In this
paper, we present a sufficient condition under which the pullback attractors
are degenerate. That is, if the Grashof constant is small enough, the pullback
attractor will be a single point on a unique, complete, bounded, strong
solution. We then apply our results to provide a new proof of the existence of
a unique, strong, periodic solution to the 3D Navier-Stokes with a small,
periodic forcing term
Mixtures: Sequential Stability of Variational Entropy Solutions

The purpose of this work is to analyze the mathematical model governing motion of n-component, heat conducting reactive mixture of compressible gases. We prove sequential stability of weak variational entropy solutions when the state equation essentially depends on the species concentration and the species diffusion fluxes depend on gradients of partial pressures. Of crucial importance for our analysis is the fact that viscosity coefficients vanish on vacuum and the source terms enjoy the admissibility condition dictated by the second law of thermodynamics
On Linear Instability and Stability of the Rayleigh-Taylor Problem in
  Magnetohydrodynamics

We investigate the stabilizing effects of the magnetic fields in the
linearized magnetic Rayleigh-Taylor (RT) problem of a nonhomogeneous
incompressible viscous magnetohydrodynamic fluid of zero resistivity in the
presence of a uniform gravitational field in a three-dimensional bounded
domain, in which the velocity of the fluid is non-slip on the boundary. By
adapting a modified variational method and careful deriving \emph{a priori}
estimates, we establish a criterion for the instability/stability of the
linearized problem around a magnetic RT equilibrium state. In the criterion, we
find a new phenomenon that a sufficiently strong horizontal magnetic field has
the same stabilizing effect as that of the vertical magnetic field on growth of
the magnetic RT instability. In addition, we further study the corresponding
compressible case, i.e., the Parker (or magnetic buoyancy) problem, for which
the strength of a horizontal magnetic field decreases with height, and also
show the stabilizing effect of a sufficiently large magnetic field.Comment: 33 page
Local well-posedness for the Hall-MHD equations with fractional magnetic
  diffusion

The Hall-magnetohydrodynamics (Hall-MHD) equations, rigorously derived from
kinetic models, are useful in describing many physical phenomena in geophysics
and astrophysics. This paper studies the local well-posedness of classical
solutions to the Hall-MHD equations with the magnetic diffusion given by a
fractional Laplacian operator, $(-\Delta)^\alpha$. Due to the presence of the
Hall term in the Hall-MHD equations, standard energy estimates appear to
indicate that we need $\alpha\ge 1$ in order to obtain the local
well-posedness. This paper breaks the barrier and shows that the fractional
Hall-MHD equations are locally well-posed for any $\alpha>\frac12$. The
approach here fully exploits the smoothing effects of the dissipation and
establishes the local bounds for the Sobolev norms through the Besov space
techniques. The method presented here may be applicable to similar situations
involving other partial differential equations.Comment: 13 pages, this version improves the previous on
Abridged continuous data assimilation for the 2D Navier-Stokes equations
  utilizing measurements of only one component of the velocity field

We introduce a continuous data assimilation (downscaling) algorithm for the
two-dimensional Navier-Stokes equations employing coarse mesh measurements of
only one component of the velocity field. This algorithm can be implemented
with a variety of finitely many observables: low Fourier modes, nodal values,
finite volume averages, or finite elements. We provide conditions on the
spatial resolution of the observed data, under the assumption that the observed
data is free of noise, which are sufficient to show that the solution of the
algorithm approaches, at an exponential rate asymptotically in time, to the
unique exact unknown reference solution, of the 2D Navier-Stokes equations,
associated with the observed (finite dimensional projection of) velocity
Global well-posedness of the 2D Boussinesq equations with fractional
  Laplacian dissipation

As a continuation of the previous work [40], in this paper we focus on the
Cauchy problem of the two-dimensional (2D) incompressible Boussinesq equations
with fractional Laplacian dissipation. We give an elementary proof of the
global regularity of the smooth solutions of the 2D Boussinesq equations with a
new range of fractional powers of the Laplacian. The argument is based on the
nonlinear lower bounds for the fractional Laplacian established in [12].
Consequently, this result significantly improves the recent works [12, 38, 40].Comment: This version fix several typos of the previous one. 25 page
The pressure in a deep-water Stokes wave of greatest height

In this paper we investigate the qualitative behaviour of the pressure
function beneath an extreme Stokes wave over infinite depth. The presence of a
stagnation point at the wave-crest of an extreme Stokes wave introduces a
number of mathematical difficulties resulting in the irregularity of the free
surface profile. It will be proven that the pressure decreases in the
horizontal direction between a crest-line and subsequent trough-line, except
along these lines themselves where the pressure is stationary with respect to
the horizontal coordinate. In addition we will prove that the pressure strictly
increases with depth throughout the fluid body.Comment: 12 pages, 2 figures. To appear in Journal of Mathematical Fluid
  Mechanic
Analysis of a time implicit scheme for the Oseen model driven by nonlinear slip boundary conditions

This work is concerned with the time discrete analysis of the Oseen system of equations driven by nonlinear slip
boundary conditions of friction type. We study the existence of solutions of the time discrete model and derive several a priori
estimates needed to recover the solution of the continuous problem by means of weak compactness. Moreover, for the
difference between the exact and approximate solutions, we obtainhttp://link.springer.com/journal/212017-12-31hb2016Mathematics and Applied Mathematic
A singular limit problem for rotating capillary fluids with variable
  rotation axis

In the present paper we study a singular perturbation problem for a
Navier-Stokes-Korteweg model with Coriolis force. Namely, we perform the
incompressible and fast rotation asymptotics simultaneously, while we keep the
capillarity coefficient constant in order to capture surface tension effects in
the limit. We consider here the case of variable rotation axis: we prove the
convergence to a linear parabolic-type equation with variable coefficients. The
proof of the result relies on compensated compactness arguments. Besides, we
look for minimal regularity assumptions on the variations of the axis.Comment: Section 5 of the previous version was remove
Pressure transfer functions for interfacial fluid problems

We make a consistent derivation, from the governing equations, of the
pressure transfer function in the small-amplitude Stokes wave regime and the
hydrostatic approximation in the small-amplitude solitary water wave regime, in
the presence of a background shear flow. The results agree with the well-known
formulae in the zero vorticity case,but they incorporate the effects of
vorticity through solutions to the Rayleigh equation. We extend the results to
permit continuous density stratification and to internal waves between two
constant-density fluids. Several examples are discussed.Comment: 20 page
Incompressible Euler Equations and the Effect of Changes at a Distance

Because pressure is determined globally for the incompressible Euler
equations, a localized change to the initial velocity will have an immediate
effect throughout space. For solutions to be physically meaningful, one would
expect such effects to decrease with distance from the localized change, giving
the solutions a type of stability. Indeed, this is the case for solutions
having spatial decay, as can be easily shown. We consider the more difficult
case of solutions lacking spatial decay, and show that such stability still
holds, albeit in a somewhat weaker form.Comment: Revised statement of Theorem 1 to include a missing definitio
An Eulerian-Lagrangian Form for the Euler Equations in Sobolev Spaces

In 2000 Constantin showed that the incompressible Euler equations can be
written in an "Eulerian-Lagrangian" form which involves the back-to-labels map
(the inverse of the trajectory map for each fixed time). In the same paper a
local existence result is proved in certain H\"older spaces $C^{1,\mu}$.
  We review the Eulerian-Lagrangian formulation of the equations and prove that
given initial data in $H^s$ for $n\geq2$ and $s>\frac{n}{2}+1$, a unique
local-in-time solution exists on the $n$-torus that is continuous into $H^s$
and $C^1$ into $H^{s-1}$. These solutions automatically have $C^1$
trajectories.
  The proof here is direct and does not appeal to results already known about
the classical formulation. Moreover, these solutions are regular enough that
the classical and Eulerian-Lagrangian formulations are equivalent, therefore
what we present amounts to an alternative approach to some of the standard
theory.Comment: 17 pages, to appear in J. Math. Fluid Mech. Lemmas 4 and 6 revised,
  several minor change