On the local well-posedness and blow-up criterion of the equations related to the 212$2\frac{1}{2}$ dimensional Lüst model

Abstract

In this paper, we investigate a two-dimensional model closely related to the dimensional L & uuml;st model with the aim of elucidating the nonlinear structure of the L & uuml;st model in more detail. To do so, we replace one of the Laplacians with a fractional Laplacian and show the existence of a unique local-in-time strong solution and establish a blow-up criterion.