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| UNIFORM STABILITY AND ASYMPTOTIC BEHAVIOR OFSOLUTIONS OF 2-DIMENSIONAL MAGNETOHYDRODYNAMICS EQUATIONS |
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Citation： |
Zhang Linghai.UNIFORM STABILITY AND ASYMPTOTIC BEHAVIOR OFSOLUTIONS OF 2-DIMENSIONAL MAGNETOHYDRODYNAMICS EQUATIONS[J].Chinese Annals of Mathematics B,1998,19(1):35~58 |
| Page view： 922
Net amount： 755 |
Authors： |
Zhang Linghai; |
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| Abstract： |
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
$H^2, L^1\cap H^2$ with $\int(u_0, A_0)dx\not= 0$, or $L^1\cap H^2$
with $\int(u_0, A_0)dx=0$, respectively. Most of the decay
rates in these estimates are optimal. Moreover, the author proves
various uniform stability results, like $\sup_{t>0}\|(w, E, r)(t))\|_Y
\le C\|(w_0, E_0)\|_X$, where $X$ and $Y$ are Sobolev spaces.
It should be pointed out that the decay estimates of the solutions for the case
$(u_0, A_0)\in L^1\cap H^2$ follow from the uniform stability
estimates. The author utilizes the Fourier splitting method
invented by Professor Schonbek and the new elaborate global energy estimates. |
Keywords： |
Uniform stability, Asymptotic behavior, Magnetohydrodynamics equations Fourier transform, Energy estimates |
Classification： |
35B, 35K, 35Q, 76W |
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