Norm inflation for the viscous nonlinear wave equation

Abstract

In this article, we study the ill-posedness of the viscous nonlinear wave equation for any polynomial nonlinearity in negative Sobolev spaces. In particular, we prove a norm inflation result above the scaling critical regularity in some cases. We also show failure of \(C^k\)-continuity, for k the power of the nonlinearity, up to some regularity threshold.