Dispersive blow-up for solutions to three dimensional generalized Zakharov-Kuznetsov equations

Abstract

We illustrate the dispersive blow up phenomena of the solutions of three dimensional generalized Zakharov-Kuznetsov equations. In particular, we construct smooth initial data such that, the associated global solutions fail to be $C^1$ at time $t$ in a null set containing all rational numbers, but are $C^1$ at all times $t$ which are generic irrational numbers. The key ingredient are to construct linear solutions which exhibit such phenomena and to prove nonlinear smoothing estimates for the full nonlinear model.

arXiv comment26 pages