On finite time blow-up for a 3D Davey-Stewartson system

TL;DR

This paper investigates conditions under which solutions to a 3D Davey-Stewartson system become singular in finite time, using distribution theory and convexity methods to establish blow-up criteria.

Contribution

It provides new sufficient conditions for finite time blow-up solutions in non-isotropic spaces for the 3D Davey-Stewartson system, extending previous understanding.

Findings

Identifies conditions leading to finite time blow-up.

Utilizes distribution theory with homogeneous symbols.

Employs convexity arguments to prove blow-up.

Abstract

We consider the elliptic-elliptic Davey-Stewartson system in the three-dimensional Euclidean space, and we give sufficient conditions for the existence of finite time blow-up solutions in non-isotropic spaces. The proof is based on some general results on distributions defined via homogeneous symbols, in conjunction with a convexity argument.