Strong solutions to the incompressible magnetohydrodynamic equations
نویسندگان
چکیده
In this paper, we are concerned with strong solutions to the Cauchy problem for the incompressible Magnetohydrodynamic equations. By the Galerkin method, energy method and the domain expansion technique, we prove the local existence of unique strong solutions for general initial data, develop a blow-up criterion for local strong solutions and prove the global existence of strong solutions under the smallness assumption of initial data. The initial data are assumed to satisfy a natural compatibility condition and allow vacuum to exist. Copyright © 2010 John Wiley & Sons, Ltd.
منابع مشابه
Global Strong Solution to the Three-dimensional Stochastic Incompressible Magnetohydrodynamic Equations
The three-dimensional incompressible magnetohydrodynamic equations with stochastic external forces are considered. First, the existence and uniqueness of local strong solution to the stochastic magnetohydrodynamic equations are proved when the external forces satisfy some conditions. The proof is based on the contraction mapping principle, stopping time and stochastic estimates. The strong solu...
متن کاملLow Mach Number Limit of Viscous Compressible Magnetohydrodynamic Flows
The relationship between the compressible magnetohydrodynamic flows with low Mach number and the incompressible magnetohydrodynamic flows is investigated. More precisely, the convergence of weak solutions of the compressible isentropic viscous magnetohydrodynamic equations to the weak solutions of the incompressible viscous magnetohydrodynamic equations is proved as the density becomes constant...
متن کاملBKM’s Criterion and Global Weak Solutions for Magnetohydrodynamics with Zero Viscosity
In this paper we derive a criterion for the breakdown of classical solutions to the incompressible magnetohydrodynamic equations with zero viscosity and positive resistivity in R3. This result is analogous to the celebrated Beale-KatoMajda’s breakdown criterion for the inviscid Eluer equations of incompressible fluids. In R2 we establish global weak solutions to the magnetohydrodynamic equation...
متن کاملCombined Incompressible and Inviscid Limit of the Compressible Magnetohydrodynamic Equations in the Whole Space
Abstract. This paper is concerned with the combined incompressible and inviscid limit of the compressible magnetohydrodynamic equations in the whole space with general initial data. It is rigorously showed that, as the Mach number, the shear viscosity coefficient and the magnetic diffusion coefficient simultaneously go to zero, the weak solution of the compressible magnetohydrodynamic equations...
متن کاملGlobal unique solvability of 3D MHD equations in a thin periodic domain
We study magnetohydrodynamic equations for a viscous incompressible resistive fluid in a thin 3D domain. We prove the global existence and uniqueness of solutions corresponding to a large set of initial data from Sobolev type space of the order 1/2 and forcing terms from L2 type space. We also show that the solutions constructed become smoother for positive time and prove the global existence o...
متن کامل