note on solution regularity of the generalized magnetohydrodynamic equations with partial dissipation abstract in this brief note we study the n dimensional magnetohydrodynamic equations with hyper viscosity and zero resistivity we prove global regularity of solutions when the hyper viscosity is sufficiently strong

on global regularity of 2d generalized magnetohydrodynamic equations abstract in this article we study the global regularity of 2d generalized magnetohydrodynamic equations 2d gmhd in which the dissipation terms are u and b we show that smooth solutions are global in the following three cases 1 2 1 0 1 2 2 2 2 0 we also show that in the inviscid case 0 if 1 then smooth solutions are global as long as the direction of the magnetic field remains smooth enough

global regularity for the 2d mhd equations with mixed partial dissipation and magnetic diffusion abstract whether or not classical solutions of the 2d incompressible mhd equations without full dissipation and magnetic diffusion can develop finite time singularities is a difficult issue a major result of this paper establishes the global regularity of classical solutions for the mhd equations with mixed partial dissipation and magnetic diffusion in addition the global existence conditional regularity and uniqueness of a weak solution is obtained for the 2d mhd equations with only magnetic diffusion

on the global regularity of generalized leray alpha type models abstract we generalize leray alpha type models studied in cheskidov et al 2005 1 and linshiz and titi 2007 4 via fractional laplacians and employ besov space techniques to obtain global regularity results with the logarithmically supercritical dissipation

dissipative quasi geostrophic equation for large initial data in the critical sobolev space the critical and super critical dissipative quasi geostrophic equations are investigated in mathbb r 2 we prove local existence of a unique regular solution for arbitrary initial data in h2 2 which corresponds to the scaling invariant space of the equation we also consider the behavior of the solution near t 0 in the sobolev space

the beale kato majda criterion for the 3d magneto hydrodynamics equations we study the blow up criterion of smooth solutions to the 3d mhd equations by means of the littlewood paley decomposition we prove a beale kato majda type blow up criterion of smooth solutions via the vorticity of velocity only namely sup j in mathbb z int 0 t delta j nabla times u infty dt where j is the frequency localization operator in the littlewood paley decomposition

generalized mhd equations abstract solutions of the d dimensional generalized mhd gmhd equations t u u u p b b u t b u b b u b are studied in this paper we pay special attention to the impact of the parameters and on the regularity of solutions our investigation is divided into three major cases 1 0 and 0 2 0 and 0 and 3 0 and 0 when 0 and 0 the gmhd equations with any 0 and 0 possess a global weak solution corresponding to any l2 initial data furthermore weak solutions associated with 1 2 d 4 and 1 2 d 4 are actually global classical solutions when their initial data are sufficiently smooth as a special consequence smooth solutions of the 3d gmhd equations with 5 4 and 5 4 do not develop finite time singularities the study of the gmhd equations with 0 and 0 is motivated by their potential applications in magnetic reconnection a local existence result of classical solutions and several global regularity conditions are established for this case these conditions are imposed on either the vorticity u or the current density j b but not both and are weaker than some of current existing ones when 0 and 0 the gmhd equations reduce to the ideal mhd equations it is shown here that the ideal mhd equations admit a unique local solution when the prescribed initial data is in a holder space cr with r 1

global regularity of the generalized liquid crystal model with fractional diffusion abstract in this paper we consider the global regularity for a n dimensional generalized liquid crystal system with fractional diffusion term 2 u for the velocity field where u g u and g 2 c 0 log e for 1 n 2 this paper provides a global regularity result for the generalized liquid crystal equations which extends the result given by jin zhu and jin to the case 0 for n 2 jin et al 2015 5

on the regularity of weak solutions to the magnetohydrodynamic equations abstract in this paper we study the regularity of weak solution to the incompressible magnetohydrodynamic equations we obtain some sufficient conditions for regularity of weak solutions to the magnetohydrodynamic equations which is similar to that of incompressible navier stokes equations moreover our results demonstrate that the velocity field of the fluid plays a more dominant role than the magnetic field does on the regularity of solution to the magneto hydrodynamic equations

global regularity of 2d leray alpha regularized incompressible magneto micropolar equations abstract in this paper we consider a cauchy problem of the 2d leray regularized incompressible magneto micropolar equations the global smooth solution of the cauchy problem for the equations with zero angular viscosity and zero magnetic diffusion or with only angular viscosity and magnetic diffusion are established

two regularity criteria for the 3d mhd equations this work establishes two regularity criteria for the 3d incompressible mhd equations the first one is in terms of the derivative of the velocity field in one direction while the second one requires suitable boundedness of the derivative of the pressure in one direction

global well posedness for a modified dissipative surface quasi geostrophic equation in the critical sobolev space h1 abstract in this paper we consider the following modified quasi geostrophic equations mqg t u 0 u 1 r where 0 1 is a fixed parameter this equation was recently introduced by p constantin g iyer and j wu 2001 in 4 as a modification of the classical quasi geostrophic equation in this paper we prove that for any initial data in the sobolev space h 1 r 2 eq mqg has a global and smooth solution in c r h 1 r 2

a maximum principle applied to quasi geostrophic equations we study the initial value problem for dissipative 2d quasi geostrophic equations proving local existence global results for small initial data in the super critical case decay of lp norms and asymptotic behavior of viscosity solution in the critical case our proofs are based on a maximum principle valid for more general flows

remarks on the global regularity of the two dimensional magnetohydrodynamics system with zero dissipation abstract we study the two dimensional magnetohydrodynamics system with generalized dissipation and diffusion in terms of fractional laplacians it is known that the classical magnetohydrodynamics system with full laplacians in both dissipation and diffusion terms admits a unique global strong solution pair making use of the special structure of the system in the two dimensional case we show in particular that the solution pair remains smooth when we have zero dissipation but only magnetic diffusion with its power of the fractional laplacian 3 2

determining targets for multi stage adaptive tests using integer programming this paper considers a multi stage adaptive test mst where the testlets at each stage are determined prior to the administration the assembly of a mst requires target information and target response functions for the mst design the targets are chosen to create tests with accurate scoring and high utilization of items in an operational pool forcing all msts to have information and response function plots to be within an interval about the targets will yield parallel msts in the sense that standardized paper and pencil tests are considered parallel the objective of this paper is to present a method to determine targets for the mst design based on an item pool and an assumed distribution of examinee ability the approach is applied to a skills readiness inventory test designed to identify logical reasoning deficiencies of examinees this method can be applied to obtain item response theory targets for a linear test as this is a special case of a mst

the 3d incompressible magnetohydrodynamic equations with fractional partial dissipation abstract the magnetohydrodynamic mhd equations have played pivotal roles in the study of many phenomena in geophysics astrophysics cosmology and engineering the fundamental problem of whether or not classical solutions of the 3d mhd equations can develop finite time singularities remains an outstanding open problem mathematically this problem is supercritical in the sense that the 3d mhd equations do not have enough dissipation if we replace the standard velocity dissipation u and the magnetic diffusion b by u and b respectively the resulting equations with 5 4 and 5 2 then always have global classical solutions an immediate issue is whether or not the hyperdissipation can be further reduced this paper shows that the global regularity still holds even if there is only directional velocity dissipation and horizontal magnetic diffusion h 5 4 b where h 1 2 2 2

the resistive magnetohydrodynamic equation near an equilibrium abstract this work intends to understand the stability and large time behavior of perturbations near a stationary solution of the 2d resistive magnetohydrodynamic mhd equation the stationary solution is taken to be a background magnetic field parallel to the horizontal axis we obtain three main results the first result assesses the stability and the precise large time asymptotic behavior for solutions to the linearzied system satisfied by the perturbation due to the lack of viscosity the standard energy estimates do not work and the proof is achieved by constructing a suitable lyapunov function the second result makes use of the special wave structure of the linearization to establish the linear stability and decay rates the third result obtains the h 1 stability for the full nonlinear system and shows that the l q norm q 2 of the magnetic field perturbation b and the l 2 norm of the gradient of b approach zero as t

logarithmically extended global regularity result of lans alpha mhd system in two dimensional space abstract we study the two dimensional generalized lans alpha magnetohydrodynamics system we show that the solution pairs of velocity and magnetic fields to this system preserve their initial regularity in two cases dissipation logarithmically weaker than a full laplacian and zero diffusion zero dissipation and diffusion logarithmically weaker than a full laplacian

a remark on global regularity of 2d generalized magnetohydrodynamic equations abstract in this paper we study the global regularity of the following 2d two dimensional generalized magnetohydrodynamic equations u t u u p b b u b t u b b u b and get global regular solutions when 0 1 2 1 3 2 3 which improves the results in 5 in particular we obtain the global regularity of the 2d generalized mhd when 0 and 3 2

global regularity for a class of 2d tropical climate model abstract in this paper we establish the global regularity of a modified version of the tropical climate model originally derived by frierson majda pauluis 2004 6 which couples the barotropic and baroclinic modes of the velocity and the typical midtropospheric temperature in proving the global regularity to bypass the difficulty caused by the very weak dissipation any small power 0 of the barotropic mode we utilize the weakly nonlinear energy estimate approach and the maximal l t q l x p regularity for the heat kernel

remarks on the regularity criteria of generalized mhd and navier stokes systems we study the regularity criteria of the three dimensional generalized magnetohydrodynamics mhd and navier stokes systems in particular we show that the regularity criteria of the generalized mhd system may be reduced to depend only on two diagonal entries of the jacobian matrix of the velocity vector field or one vorticity component and one entry of the jacobian matrix of the velocity vector field

kinetic boundary conditions in the lattice boltzmann method derivation of the lattice boltzmann method from the continuous kinetic theory x he and l s luo phys rev e 55 r6333 1997 x shan and x he phys rev lett 80 65 1998 is extended in order to obtain boundary conditions for the method for the model of a diffusively reflecting moving solid wall the boundary condition for the discrete set of velocities is derived and the error of the discretization is estimated numerical results are presented which demonstrate convergence to the hydrodynamic limit in particular the knudsen layer in the kramers problem is reproduced correctly for small knudsen numbers

the maximum principle and the global attractor for the dissipative 2d quasi geostrophic equations the long time behavior of the solutions to the two dimensional dissipative quasi geostrophic equations is studied we obtain a new positivity lemma which improves a previous version of a cordoba and d cordoba 10 and 11 as an application of the new positivity lemma we obtain the new maximum principle i e the decay of the solution in l p for any p 2 when f is zero as a second application of the new positivity lemma for the sub critical dissipative case with open image in new window the existence of the global attractor for the solutions in the space h s for any s 2 1 is proved for the case when the time independent f is non zero therefore the global attractor is infinitely smooth if f is this significantly improves the previous result of berselli 2 which proves the existence of an attractor in some weak sense for the case 1 the global attractor exists in h s for any s 0 and the estimate of the hausdorff and fractal dimensions of the global attractor is also available

remarks on the blow up criteria for three dimensional ideal magnetohydrodynamics equations in this paper we establish some improved regularity conditions for the three dimensional 3d magnetohydrodynamics equations we proved the logarithmically improved caflisch klapper steele s criteria remarks on sigularities dimension and energy dissipation for ideal hydrodynamics and mhd commun math phys 184 443 1997 as well as the logarithmically improved he xin s on the regularity of weak solutions to the magnetohydrodynamic equations j differ equ 23 235 2005 and wu s bounds and new approach for the 3d mhd equations j nonlinear sci 12 395 2002 results for 3d ideal mhd equations

on the global regularity of two dimensional generalized magnetohydrodynamics system abstract we study the two dimensional generalized magnetohydrodynamics system with dissipation and diffusion in terms of fractional laplacians in particular in the case where the diffusion term has the power 1 in contrast to the previous result of 1 2 we show that 1 3 suffices in order for the solution pair of velocity and magnetic fields to remain smooth for all time

on the regularity of a class of generalized quasi geostrophic equations abstract in this article we consider the following generalized quasi geostrophic equation t u 0 u r x r 2 where 0 0 1 and 0 2 we first show a general conditional criterion yielding the nonlocal maximum principles for the whole space active scalars then mainly by applying the general criterion for the case 0 1 and 1 2 we obtain the global well posedness of the system with smooth initial data and for the case 0 1 and 2 1 we prove the local smoothness and the eventual regularity of the weak solution of the system with appropriate initial data

remarks on the regularity criteria of three dimensional magnetohydrodynamics system in terms of two velocity field components we study the three dimensional magnetohydrodynamics system and obtain its regularity criteria in terms of only two velocity vector field components eliminating the condition on the third component completely the proof consists of a new decomposition of the four nonlinear terms of the system and estimating a component of the magnetic vector field in terms of the same component of the velocity vector field this result may be seen as a component reduction result of many previous works c he and z xin on the regularity of weak solutions to the magnetohydrodynamic equations j differ equ 213 2 234 254 2005 y zhou remarks on regularities for the 3d mhd equations discrete contin dyn syst 12 5 881 886 2005

some mathematical questions related to the mhd equations some questions relating to the large time behavior of the solutions of mhd equations for a viscous incompressible resistive fluid are investigated the physical system is briefly described and the functional setting of the equations a flow in a bounded domain or in whole space with a space periodicity property in all directions the main existence and uniqueness results for weak and strong solutions of the mhd equations are recalled regularity properties and bounds on the solutions to the equations which are valid for all time are established and the concept of functional invariant sets is introduced which is contained in the space of smooth functions if the data are sufficiently regular the squeezing property of the trajectories are stated and it is shown that any functional invariant set for the mhd equations and in particular any attractor has a finite haussdorf dimension the flow is found to be totally determined for large dimensions by a finite number of parameters 26 references