Existence theory and LpLp estimates for the solution of nonlinear viscous wave equation

In this paper, we consider the global existence of the Cauchy problem for the nonlinear viscous wave equation. We apply the approach introduced in Li and Chen (1989) [15] and get the global existence theory directly by using the decaying properties of the solution. Such properties are obtained by long wave–short wave decomposition  , Green’s function method and energy estimates. Finally, we show the LpLp estimates for the solution by interpolation lemma.