Global small solutions to the compressible 2D magnetohydrodynamic system without magnetic diffusion

This work establishes the global existence and uniqueness of smooth solutions to the two-dimensional compressible magnetohydrodynamic system when the initial data is close to an equilibrium state. In addition, explicit large-time decay rates for various Sobolev norms of the solutions are also obtained. These results are achieved through a new approach of diagonalizing a system of coupled linearized equations. The standard method of diagonalization via the eigenvalues and eigenvectors of the matrix symbol is very difficult to implement here. This new process allows us to obtain an integral representation of the full system through explicit kernels. In addition, in order to overcome various difficulties such as the anisotropicity and criticality, we fully exploit the structure of the integral representation and employ extremely delicate Fourier analysis and associated estimates.

举办单位：数学与统计学院

发 布 人：科研助理 发布时间： 2017-07-15

发 布 人：科研助理 发布时间： 2017-07-15

吴奕飞，天津大学应用数学中心特聘研究员，博士生导师。在Advance in Math.，SIAM J Math.Anal.,JDE 等国际著名数学杂志上发表了多篇PDE研究论文。东北师范大学大应用数学实验室特邀报告人。