Construction of blow-up solutions for Zakharov system on ${\mathbb{T}}^2$

Abstract

We consider the Zakharov system in two space dimension with periodic boundary condition. We prove the existence of finite time blow-up solutions. Further, we show there exists no minimal mass blow-up solution.

39 pages

References in corpus (2)

• Local well-posedness for the Zakharov system on multidimensional torus
• Blow up in several points for the nonlinear Schrödinger equation on a bounded domain

Cited by in corpus (2)

• The fourth order nonlinear Schrodinger limit for quantum Zakharov system
• Resonant decomposition and the $I$-method for the two-dimensional Zakharov system