论文标题
$ \ r^2 $中电交流模型解决方案的长时间行为
Long Time Behavior of Solutions of an Electroconvection Model in $\R^2$
论文作者
论文摘要
我们考虑了一个二维电转配模型，该模型由非线性和非局部系统组成，该系统耦合了电荷分布和流体的演变。我们表明，$ l^2（\ rr^2）$的解决方案的时间与线性未耦合系统相同的速率相同。这是通过证明非线性演化和线性演化之间的差异比线性演化更快的。为了证明急剧的$ l^2 $衰减，我们在$ h^2（\ rr^2）$中建立了衰减的界限，并在充电密度的二次时刻的时间内建立了对数增长。
We consider a two dimensional electroconvection model which consists of a nonlinear and nonlocal system coupling the evolutions of a charge distribution and a fluid. We show that the solutions decay in time in $L^2(\Rr^2)$ at the same sharp rate as the linear uncoupled system. This is achieved by proving that the difference between the nonlinear and linear evolution decays at a faster rate than the linear evolution. In order to prove the sharp $L^2$ decay we establish bounds for decay in $H^2(\Rr^2)$ and a logarithmic growth in time of a quadratic moment of the charge density.
