Global existence and exponential decay to equilibrium for DLSS-type equations

TL;DR

This paper proves global existence, convergence to equilibrium, and spatial analyticity for one- and multi-dimensional DLSS-type equations, advancing understanding of their long-term behavior in critical spaces.

Contribution

It provides a unified analysis demonstrating global solutions and exponential decay for both extended one-dimensional and multi-dimensional DLSS equations.

Findings

Global existence of solutions in critical spaces

Convergence to equilibrium with exponential decay

Gain of spatial analyticity for solutions

Abstract

In this paper, we deal with two logarithmic fourth order differential equations: the extended one-dimensional DLSS equation and its multi-dimensional analog. We show the global existence of solution in critical spaces, its convergence to equilibrium and the gain of spatial analyticity for these two equations in a unified way.