三维带有衰减项的不可压缩磁流体力学方程组弱解与强解的研究

Study on Weak Solution and Strong Solution of Incompressible MHD Equations with Damping in Three-Dimensional Systems

论文研究了带有衰减项的磁流体力学方程组的柯西问题.当β≥1及初值u0,b0∈L^2(R^3)时,采用Galerkin方法证明了方程组存在全局弱解.并且当初值u0∈H0^1∩L^β+1(R^3),b0∈H0^1(R^3)时,可以得到方程组存在唯一局部强解.

In this paper, the Cauchy problem of the MHD equations with damping is studied. When β≥1 and initial data satisfy u0,b0∈L^2(R^3), the Galerkin method is used to prove the global weak solution of the equations. When the initial data satisfy u0∈H0^1∩L^β+1(R^3),b0∈H0^1(R^3), it is possible to obtain a unique local strong solution for the equation group.