Existence, Uniqueness, Regularity and Long-term Behavior for Dissipative Systems Modeling Electrohydrodynamics
Existence, Uniqueness, Regularity and Long-term Behavior for Dissipative Systems Modeling Electrohydrodynamics
复制标题
DOI：
--
复制
发表时间：
2009-10
期刊：
影响因子：
--
通讯作者：
R. Ryham
中科院分区：
文献类型：
--
作者：
R. Ryham
研究了电流体动力学中非线性非局部方程组的耗散系统。对于二维空间中一般$\mathbf{L}^2$初始数据和三维空间中数据中的小数据，证明了解的存在唯一性和正则性。通过研究相对熵泛函的线性化，建立了三维存在性。我们还用一个速率建立了平稳解的收敛性。
We study a dissipative system of nonlinear and nonlocal equations modeling the flow of electrohydrodynamics. The existence, uniqueness and regularity of solutions is proven for general $\mathbf{L}^2$ initial data in two space dimensions and for small data in data in three space dimensions. The existence in three dimensions is established by studying a linearization of a relative entropy functional. We also establish the convergence to the stationary solution with a rate.