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In this paper, we consider the Cauchy problem to the planar non-resistive magnetohydrodynamic equations without heat conductivity, and establish the global well-posedness of strong solutions with large initial data. The key ingredient of the proof is to establish the a priori estimates on the effective viscous flux and a newly introduced transverse effective viscous flux vector field inducted by the transverse magnetic field. The initial density is assumed only to be uniformly bounded and of finite mass and, in particular, the vacuum and discontinuities of the density are allowed.
This paper is concerned with the asymptotic behaviors of global strong solutions to the incompressible non-resistive viscous magnetohydrodynamic (MHD) equations with large initial perturbations in two-dimensional periodic domains in Lagrangian coordi
In this paper, we investigate the convergence of the global large solution to its associated constant equilibrium state with an explicit decay rate for the compressible Navier-Stokes equations in three-dimensional whole space. Suppose the initial dat
We are considering the asimptotic behavior as $ttoinfty$ of solutions of the Cauchy problem for parabolic second order equations with time periodic coefficients. The problem is reduced to considering degenerate time-homogeneous diffusion processes on the product of a unit circle and Euclidean space.
We prove the existence of a large class of global-in-time expanding solutions to vacuum free boundary compressible Euler flows without relying on the existence of an underlying finite-dimensional family of special affine solutions of the flow.
We study the existence and uniqueness of global strong solutions to the equations of an incompressible viscoelastic fluid in a spatially periodic domain, and show that a unique strong solution exists globally in time if the initial deformation and ve