摘要
This paper is concerned with uniform stability and asymptotic behavior for solutions of 2-dimensional Magnetohydrodynamics equations. The author establishes the corresponding temporal decay estimates when the initial data is in the following Sobolev spaces H 2, L 1∩H 2 with ∫(u 0, A 0)dx≠0, or L 1∩H 2 with ∫(u 0, A 0)dx=0, respectively. Most of the decay rates in these estimates are optimal. Moreover, the author proves various uniform stability results, like sup t>0 ‖(w, E, r)(t))‖ YC‖(w 0, E 0)‖ X, where X and Y are Sobolev spaces. It should be pointed out that the decay estimates of the solutions for the case (u 0, A 0)∈L 1∩H 2 follow from the uniform stability estimates. The author utilizes the Fourier splitting method invented by Professor Schonbek and the new elaborate global energy estimates.
This paper is concerned with uniform stability and asymptotic behavior for solutions of 2-dimensional Magnetohydrodynamics equations. The author establishes the corresponding temporal decay estimates when the initial data is in the following Sobolev spaces H 2, L 1∩H 2 with ∫(u 0, A 0)dx≠0, or L 1∩H 2 with ∫(u 0, A 0)dx=0, respectively. Most of the decay rates in these estimates are optimal. Moreover, the author proves various uniform stability results, like sup t>0 ‖(w, E, r)(t))‖ YC‖(w 0, E 0)‖ X, where X and Y are Sobolev spaces. It should be pointed out that the decay estimates of the solutions for the case (u 0, A 0)∈L 1∩H 2 follow from the uniform stability estimates. The author utilizes the Fourier splitting method invented by Professor Schonbek and the new elaborate global energy estimates.
