| 赵继红,李秀蓉.一类耗散型电流体动力学方程组自相似解的渐近稳定性[J].数学年刊A辑,2019,(1):055~78 |
| 一类耗散型电流体动力学方程组自相似解的渐近稳定性 |
| Asymptotic Stability of Self-similar Solutions for Dissipative Systems Modeling Electrohydrodynamics |
| Received:March 27, 2017 Revised:January 03, 2018 |
| DOI：10.16205/j.cnki.cama.2019.0006 |
| 中文关键词: Electrohydrodynamics, Lorentz spaces, Self-similar solution, Asymptotic stability |
| 英文关键词:Electrohydrodynamics, Lorentz spaces, Self-similar solution, Asymptotic stability |
| 基金项目: |
| Author Name | Affiliation | E-mail | | ZHAO Jihong | School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, Shaanxi, China
College of Science, Northwest AF University, Yangling 712100, Shaanxi, China. | jihzhao@163.com | | LI Xiurong | College of Science, Northwest AF University, Yangling 712100, Shaanxi, China. | 18435154219@163.com |
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| 中文摘要: |
| 主要考虑一类来源于电流体动力学中的由非线性非局部方程组耦合而成的耗散型系统的初值问题.
利用Lorentz空间中广义$L^p$-$L^q$热半群估计和广义Hardy-Littlewood-Sobolev不等式, 首先证明了该系统在Lorentz空间中自相似解的整体存在性和唯一性, 然后建立了自相似解当时间趋于无穷时的渐近稳定性. 因为Lorentz空间包含了具有奇性的齐次函数, 因次上述结果保证了具有奇性的初值所对应的自相似解的整体存在性和渐近稳定性. |
| 英文摘要: |
| The authors consider a dissipative system of nonlinear and nonlocal equations modeling the flow of electrohydrodynamics in
the whole space $\mathbb{R}^{n}$, $n\ge3$. By making use of the generalized $L^p$-$L^q$ heat semigroup estimates in the Lorentz spaces and the
generalized Hardy-Littlewood-Sobolev inequality, the authors first prove global existence and uniqueness of self-similar solution in the Lorentz
spaces, then establish the asymptotic stability of self-similar solutions as time goes to infinity. Since the authors Cope with the initial data in
the Lorentz spaces, the existence of self-similar solutions provided the initial data are small homogeneous functions. |
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