Large time behavior of the compressible magnetohydrodynamic equations with Coulomb force
Large time behavior of the compressible magnetohydrodynamic equations with Coulomb force
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DOI：
10.1016/j.jmaa.2015.02.077
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发表时间：
2015-07
影响因子：
1.3
通讯作者：
Zhong Tan;Leilei Tong;Yong Wang
中科院分区：
文献类型：
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作者：
Zhong Tan;Leilei Tong;Yong Wang
本文考虑了带库仑力的可压缩磁流体动力学方程的Cauchy问题在常平衡态附近解的大时性。假设初始数据的h3范数很小，但其高阶导数可能很大，通过引入负Sobolev和Besov空间，得到了解及其高阶空间导数的最优时间衰减率。作为一个直接的副产品，衰减率的L - L 2（1≤p≤2）类型不需要初始数据的L - p范数的小。
In this paper, we consider the large time behavior of the solutions near a constant equilibrium state to the Cauchy problem for the compressible magnetohydrodynamic equations with Coulomb force in R 3. Under the assumptions that the H 3 norm of the initial data is small, but its higher order derivatives could be large, we obtain the optimal time decay rates of the solutions and their higher-order spatial derivatives by introducing the negative Sobolev and Besov spaces. As an immediate byproduct, the L p–L 2 (1⩽ p⩽ 2) type of the decay rates follows without requiring the smallness for L p norm of initial data.