Instantaneous blow-up of classical solutions to the Cauchy problem for the Khokhlov–Zabolotskaya equation

Abstract

The Cauchy problem for a second-order nonlinear equation with mixed derivatives is considered. It is proved that its classical local-in-time solution does not exist. The blow-up of the solution is proved by applying S.I. Pohozaev and E.L. Mitidieri’s nonlinear capacity method.