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Derivation of the Hall-MHD Equations from the Navier–Stokes–Maxwell Equations
By using a set of scaling limits, the authors in Acheritogaray et al. (Kinet Relat Models 4:901–918, 2011) and Srinivasan and Shumlak (Phys Plasmas...
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Global Weak Solutions of Compressible Navier-Stokes-Landau-Lifshitz-Maxwell Equations for Quantum Fluids in Dimension Three
In this paper, we consider the weak solutions of compressible Navier-Stokes-Landau-Lifshitz-Maxwell (CNSLLM) system for quantum fluids with a linear...
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Local Well-Posedness and Regularity Criterion for the 3D Density-Dependent Incompressible Maxwell–Navier–Stokes System
In this paper, we prove the local well-posedness and regularity criterion of strong solutions to the 3D density-dependent incompressible...
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A Compact Course on Linear PDEs
This textbook is devoted to second order linear partial differential equations. The focus is on variational formulations in Hilbert spaces. It...
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Weak and smooth solutions to incompressible Navier-Stokes-Landau-Lifshitz-Maxwell equations
Considering the Navier-Stokes-Landau-Lifshitz-Maxwell equations, in dimensions two and three, we use Galerkin method to prove the existence of weak...
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On the Role of the Displacement Current and the Cattaneo’s Law on Boundary Layers of Plasma
In the present paper, we aim to mathematically analyse the role of the displacement current and the Cattaneo’s law on the boundary-layer theory of...
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Approximations to Isentropic Planar Magneto-Hydrodynamics Equations by Relaxed Euler-Type Systems
In this paper, the authors consider an approximation to the isentropic planar Magneto-hydrodynamics (MHD for short) equations by a kind of relaxed...
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Artificial Compressibility Method for the Navier–Stokes–Maxwell–Stefan System
The Navier–Stokes–Maxwell–Stefan system describes the dynamics of an incompressible gaseous mixture in isothermal condition. In this paper we set up...
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The Low Mach Number Limit for Isentropic Compressible Navier-Stokes Equations with a Revised Maxwell’s Law
We investigate the low Mach number limit for the isentropic compressible Navier-Stokes equations with a revised Maxwell’s law (with Galilean...
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Modeling, or where do differential equations come from
Partial differential equations describe numerous phenomena in nature, technology, medicine, economics, ... In this first chapter we shall describe...
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Finite Time Blow-Up Behaviors of Strong Solutions to the Compressible Navier-Stokes Equations
In this paper, we are interested in the finite time blow-up behaviors of strong solutions to the compressible Navier-Stokes equations with vacuum as...
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Upper and lower convergence rates for strong solutions of the 3D non-Newtonian flows associated with Maxwell equations under large initial perturbation
We show the upper and lower bounds of convergence rates for strong solutions of the 3D non-Newtonian flows associated with Maxwell equations under a...
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On Some Recent Results from the Theory of MHD Equations
This chapter shows the main ideas of the derivation of the MHD and Hall–MHD equations (Sect. 1) and provides a brief survey of qualitative properties...
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Global Smooth Solution to the Incompressible Navier-Stokes-Landau-Lifshitz Equations
In this paper, we will investigate the incompressible Navier-Stokes-Landau-Lifshitz equations, which is a system of the incompressible Navier-Stokes...
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New Analysis of Mixed Finite Element Methods for Incompressible Magnetohydrodynamics
This paper focuses on new error analysis of a class of mixed FEMs for stationary incompressible magnetohydrodynamics with the standard inf-sup stable...
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Rate-Type Models
Spatial interaction and memory effects are among the possible features of non-simple materials. As to memory effects in fluids, the inadequacy of the...
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Attractors of Hamiltonian Nonlinear Partial Differential Equations
We survey the theory of attractors of nonlinear Hamiltonian partial differential equations since its appearance in 1990. These are results on global...
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Spectral discretization of Darcy equations coupled with navier-stokes equations by vorticity-velocity-pressure formulation
We consider a model coupling the Darcy equations in a porous medium with the Navier-Stokes equations in the cracks, for which the coupling is...
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Existence results for a class of two-fold saddle point parabolic differential equations
We propose and analyze an abstract framework to study the well-posedness for a family of linear degenerate parabolic augmentedmixed equations.We...