Regularity and blow-up in a surface growth model

TL;DR

This paper investigates the regularity and potential blow-up of solutions in a scalar surface growth model, drawing parallels to the 3D Navier-Stokes equations through energy methods and Lyapunov functionals.

Contribution

It provides new regularity results and blow-up criteria for a surface growth model, highlighting similarities to the Navier-Stokes equations.

Findings

Established regularity conditions for the model

Derived blow-up criteria based on energy methods

Identified conditions under which solutions remain regular or blow up

Abstract

The paper contains several regularity results and blow-up criterions for a surface growth model, which seems to have similar properties to the 3D Navier-Stokes, although it is a scalar equation. As a starting point we focus on energy methods and Lyapunov-functionals.