The three-dimensional compressible magnetohydrodynamic equation in the whole space are studied this paper. global classical solution is established when initial data small perturbations of some given constant state. Moreover, optimal decay rate also obtained.

The low Mach number limit for the multi-dimensional full magnetohydrodynamic (MHD) equations, in which effect of thermal conduction is taken into account, rigorously justified within framework classical solutions with small density and temperature variations. Moreover, we show that a sufficiently number, compressible MHD equations admit smooth solution on time interval where incompressible exists. In addition, ideal entropy variation also investigated. convergence rates are obtained both cases.

This paper is concerned with the incompressible limit of compressible magnetohydrodynamic equations vanishing viscosity coefficients and general initial data in whole space $\mathbb{R}^d$ ($d=2$ or 3). It rigorously showed that, as Mach number, shear coefficient, magnetic diffusion coefficient simultaneously go to zero, weak solutions converge strong solution ideal long latter exists.

This paper considers the initial boundary problem to planar compressible magnetohydrodynamic equations with large data and vacuum. The global existence uniqueness of strong solutions are established when heat conductivity coefficient $κ(θ)$ satisfies \begin{document}$C_{1}(1+\theta^q)\leq \kappa(\theta)\leq C_2(1+\theta^q)$\end{document}for some constants $q>0$, $C_1,C_2>0$.

It is well known that the general radiation hydrodynamics models include two mainly coupled parts: one macroscopic fluid part, which governed by compressible Navier--Stokes--Fourier equations; another field described transport equation of photons. Under physical approximations, "gray" approximation and P1 approximation, can derive so-called Navier--Stokes--Fourier--P1 model from one. In this paper, we study nonrelativistic limit problem for due to fact speed light much larger than fluid. Our...

In a plasma, the ionic Vlasov-Poisson-Boltzmann system models evolution of ions interacting with themselves through self-consistent electrostatic potential and collisions. It distinguishes electric via an extra exponential nonlinearity in coupled Poisson-Poincar\'{e} equation which creates some essential mathematical difficulties. Despite its physical importance, global well-posedness to this remains completely open. This gap is filled article three dimensional period box case. We show that...

The full compressible magnetohydrodynamic equations can be derived formally from the complete electromagnetic fluid system in some sense as dielectric constant tends to zero. This process is usually referred approximation physical books. In this paper we justify singular limit rigorously framework of smooth solutions for well-prepared initial data.

The quasineutral limit of the Navier–Stokes–Poisson system in whole space Rd(d≥1) and torus Td is studied this paper. It shown that, for well-prepared initial data, global weak solution converges strongly to strong incompressible Navier–Stokes equations.

The compressible magnetohydrodynamic equations can be derived from the describing electromagnetic dynamics as dielectric constant tends to zero. Under assumption that initial data are well prepared, we justify this singular limit rigorously for smooth solutions fluid system in three dimensions by employing an elaborate nonlinear energy method.

This paper studies the three-dimensional density-dependent incompressible magnetohydrodynamic equations. First, a regularity criterion is proved which allows initial density to contain vacuum. Then we establish another blow-up in Besov space B˙∞,20 when positive bounded away from zero. Third, prove global nonexistence result for with high decreasing at infinity. Fourth, obtain equations domain. Finally, also give some remarks on criteria full compressible domain and homogeneous equation whole R3.

A kinetic-fluid model describing the evolutions of disperse two-phase flows is considered. The consists Vlasov--Fokker--Planck equation for particles (disperse phase) coupled with compressible Navier--Stokes equations fluid (fluid through friction force. force depends on density, which different from many previous studies models and more physical in modeling but significantly difficult analysis. New approaches techniques are introduced to deal strong coupling particles. global well-posedness...

We study the incompressible limit of compressible nonisentropic ideal magnetohydrodynamic equations with general initial data in whole space $\mathbb{R}^d$ ($d=2,3$). first establish existence classic solutions on a time interval independent Mach number. Then, by deriving uniform priori estimates, we obtain convergence solution to that as number tends zero.

The paper deals with the asymptotic limits of full compressible magnetohydrodynamic (MHD) equations in whole space $\mathbb{R}^3$ which are coupling between Navier--Stokes--Fourier system Maxwell governing behavior magnetic field. It is rigorously shown that for general initial data, weak solutions MHD converge to strong solution ideal incompressible as Mach number, viscosity coefficients, heat conductivity, and diffusion coefficient go zero simultaneously. Furthermore, convergence rates...

This paper deals with the low Mach number limit of full compressible Navier–Stokes–Maxwell system. It is justified rigorously that, for well-prepared initial data, solutions system converge to that incompressible as tends zero.

In this paper, we prove the local well-posedness of strong solutions to a compressible non-isothermal model for nematic liquid crystals in bounded domain Ω⊂R3 provided that initial data satisfy natural compatibility condition. The assumption on positivity density is not needed here, and it may vanish an open subset Ω.