Time-space $L^2$-boundedness for the 2D Navier-Stokes equations and hyperbolic Navier-Stokes equations

Abstract

In this paper, we study the Cauchy problem for the two dimensional Navier-Stokes equations and hyperbolic Navier-Stokes equations. We show the time-space $L^2$-boundedness of the solutions for initial data in $L^1$ space. The $L^2$-boundedness of solutions which proved in this paper gives better decay order in time than known results.