On the decay of solutions to the linearized equations of electro-magneto-fluid dynamics
On the decay of solutions to the linearized equations of electro-magneto-fluid dynamics
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DOI：
10.1007/bf03167068
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发表时间：
1984-12
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影响因子：
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通讯作者：
T. Umeda;S. Kawashima;Yasushi Shizuta
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文献类型：
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作者：
T. Umeda;S. Kawashima;Yasushi Shizuta
研究了导电可压缩粘性流体的线性化方程。证明了衰减估计（1+t）−3/4 inL 2（R3）对上述方程的解成立，假设初始数据是inL 2（R3）<$L1（R3）。由于方程组不是旋转不变的，单参数矩阵族的扰动理论不足以导出上述结果。因此，通过利用能量方法，我们证明了衰减估计适用于对称双曲抛物型方程的一般类的解，其中包含电磁流体动力学和磁流体动力学中的线性化方程。
The linearized equations of the electrically conducting compressible viscous fluids are studied. It is shown that the decay estimate (1+t)−3/4inL2(R3) holds for solutions of the above equations, provided that the initial data are inL2(R3)∩L1(R3). Since the systems of equations are not rotationally invariant, the perturbation theory for one parameter family of matrices is not useful enough to derive the above result. Therefore, by exploiting an energy method, we show that the decay estimate holds for the solutions of a general class of equations of symmetric hyperbolic-parabolic type, which contains the linearized equations in both electro-magneto-fluid dynamics and magnetohydrodynamics.