A lower bound on the blow-up rate for the Davey-Stewartson system on the torus

TL;DR

This paper establishes a lower bound on the rate at which solutions to the hyperbolic-elliptic Davey-Stewartson system blow up on a two-dimensional torus, specifically for certain Sobolev space regularities.

Contribution

It provides the first known lower bound on blow-up rates for the Davey-Stewartson system on a torus in the specified Sobolev spaces.

Findings

Proves a lower bound on blow-up rate for solutions in H^s, 1/2 < s < 1.

Focuses on the hyperbolic-elliptic version of the system.

Addresses blow-up behavior in a periodic setting.

Abstract

We consider the hyperbolic-elliptic version of the Davey-Stewartson system with cubic nonlinearity posed on the two dimensional torus. A natural setting for studying blow up solutions for this equation takes place in $H^s, 1/2 < s < 1$. In this paper, we prove a lower bound on the blow up rate for these regularities.