论文标题
对2D粘性浅水方程的初始数据的不均匀依赖性
Non-uniform dependence on initial data for the 2D viscous shallow water equations
论文作者
论文摘要
对数据的统一依赖性失败是双曲系统的经典解决方案的有趣属性。在本文中，我们将Cauchy问题的解决方案图视为二键蛋白寄生虫系统的2D粘性浅水方程。我们证明，此问题的解决方案图在sobolev空间中并不均匀地连续，$ h^s \ times h^{s} $对于$ s> 2 $。
The failure of uniform dependence on the data is an interesting property of classical solution for a hyperbolic system. In this paper, we consider the solution map of the Cauchy problem to the 2D viscous shallow water equations which is a hyperbolic-parabolic system. We prove that the solution map of this problem is not uniformly continuous in Sobolev spaces $H^s\times H^{s}$ for $s>2$.
