论文标题
二维Kuramoto-Sivashinsky方程的全球存在
Global existence for the two-dimensional Kuramoto-Sivashinsky equation with advection
论文作者
论文摘要
我们在二维圆环上以标态形式研究库拉莫托 - 摩托山方程式（KSE），并通过不可压缩的矢量场进行和不向后。我们证明了在L2中为任意数据的温和解决方案的局部存在。然后，我们研究全球存在的问题。我们证明，在有任意数据的对流的情况下，KSE的全球存在，前提是速度场V满足某些条件，以确保相关的高渗透 - 辅助方程的耗散时间足够小。在没有对流的情况下，只有在线性化操作员不接受任何生长模式并获得足够小的初始数据时，才能显示全局存在。
We study the Kuramoto-Sivashinsky equation (KSE) in scalar form on the two-dimensional torus with and without advection by an incompressible vector field. We prove local existence of mild solutions for arbitrary data in L2. We then study the issue of global existence. We prove global existence for the KSE in the presence of advection for arbitrary data, provided the advecting velocity field v satisfies certain conditions that ensure the dissipation time of the associated hyperdiffusion-advection equation is sufficiently small. In the absence of advection, global existence can be shown only if the linearized operator does not admit any growing mode and for sufficiently small initial data.
