Long-time solvability for the 2D dispersive SQG equation with improved regularity

Abstract

In this paper, we study the long-time existence and uniqueness (solvability) for the initial value problem of the 2D inviscid dispersive SQG equation. First we obtain the local solvability with existence-time independent of the amplitude parameter A. Then, assuming more regularity and using a blow-up criterion of BKM type and a space-time estimate of Strichartz type, we prove long-time solvability of solutions in Besov spaces for large A and arbitrary initial data. In comparison with previous results, we are able to consider improved cases of the regularity and larger initial data classes