Related papers: Optimal time decay estimation for large-solution a…
In this paper we are concerned with the global well-posedness for the compressible MHD equations with large data. We show that if the shear viscosity $\mu$ is a positive constant and the bulk viscosity $\lambda$ is the power function of the…
The authors study the Cauchy problem of the magnetohydrodynamic equations for viscous compressible barotropic flows in two or three spatial dimensions with vacuum as far field density. For two spatial dimensions, we establish the global…
We investigate the global existence and optimal time decay rate of solution to the one-dimensional (1D) two-phase flow described by compressible Euler equations coupled with compressible Navier-Stokes equations through the relaxation drag…
We address the analyticity and large time decay rates for strong solutions of the Hall-MHD equations. By Gevrey estimates, we show that the strong solution with small initial date in $H^r(\mathbb{R}^3)$ with $r>\f 52$ becomes analytic…
This paper is concerned with the Cauchy problem of the multi-dimensional incompressible magnetohydrodynamic equations with inhomogeneous density and fractional dissipation. It is shown that when $\alpha+\beta=1+\frac{n}{2}$ satisfying…
In this paper, we study the global well-posedness and optimal time decay rates of strong solutions to the diffusion approximation model in radiation hydrodynamics in $\mathbb{R}^3$. This model consists of the full compressible Navier-Stokes…
In this paper, we are concerned with the well-posedness and large time behavior of Cauchy problem for 3D incompressible Navier-Stokes-Cahn-Hilliard equations. First, using Banach fixed point theorem, we establish the local well-posedness of…
This paper resolves the global regularity problem for the three-dimensional compressible magnetohydrodynamics (MHD) equations in the three-dimensional whole space, in the presence of a background magnetic field. Motivated by geophysical…
In this paper we study the compressible magnetohydrodynamics equations in three dimensions, which offer a good model for plasmas. Formation of singularity for C1-solution in finite time is proved with axisymmetric initial data. The key…
Whether the smooth solution of the multi-dimensional viscous compressible fluids will blow-up in finite time has always been a chanllenging problem. In the recent work\cite{FM}, Merle et al. proved that there are smooth solutions to the 2D…
The equations of 2D incompressible dissipationless extended magnetohydrodynamics (XMHD) extend the equations of incompressible Hall MHD (HMHD) by retaining finite-electron inertia. These XMHD equations couple the fluid velocity ${\bf V} =…
This study delves into a comprehensive examination of the three-dimensional $(3D)$ incompressible magneto-hydrodynamic $(MHD)$ equations in $H^{1}(\R^{3})$. The modification involves incorporating a power term in the nonlinear convection…
We show that the uniform radius of spatial analyticity $\sigma(t)$ of solutions at time $t$ to the fifth order KdV-BBM equation cannot decay faster than $1/ \sqrt{t}$ for large $t$, given initial data that is analytic with fixed radius…
The present paper is dedicated to the large time asymptotic behavior of global strong solutions near constant equilibrium (away from vacuum) to the compressible Navier-Stokes-Poisson equations. Precisely, we present that under the same…
This paper focuses on an optimal error analysis of a fully discrete finite element scheme for the Cahn--Hilliard--magnetohydrodynamic (CH-MHD) system. The method use the standard inf-sup stable Taylor--Hood/MINI elements to solve the…
In this paper, we prove the global existence of smooth solutions to the three-dimensional incompressible magneto-hydrodynamical system with initial data close enough to the equilibrium state, $(e_3,0).$ Compared with the the previous works…
We consider the Cauchy problem for the generalized Zakharov-Kuznetsov-Burgers equation in 2D. This is one of the nonlinear dispersive-dissipative equations, which has a spatial anisotropic dissipative term $-\mu u_{xx}$. In this paper, we…
We consider the 3D stochastic Navier-Stokes equation on the torus. Our main result concerns the temporal and spatio-temporal discretisation of a local strong pathwise solution. We prove optimal convergence rates in for the energy error with…
A main result of this paper establishes the global stability of the 3D MHD equations with mixed partial dissipation near a background magnetic field in the domain $\Omega=\mathbb{T}^2\times\mathbb{R}$ with $\mathbb{T}^2=[0, 1]^2$. More…
We study the uniqueness, the continuity in $L^2$ and the large time decay for the Leray solutions of the $3D$ incompressible Navier-Stokes equations with nonlinear exponential damping term $a (e^{b |u|^{\bf 4}}-1)u$, ($a,b>0$).