Nonuniform dependence on initial data for the 2D viscous shallow water equations

The failure of uniform dependence on the data is an interesting property classical solution for a hyperbolic system. In this paper, we consider map Cauchy problem to 2D viscous shallow water equations, which hyperbolic–parabolic We give new approach studying issue nonuniform initial these equations. prove that not uniformly continuous in Sobolev spaces H s × $H^s\times H^{s}$ > 2 $s>2$ .