Spatial behavior of solutions for a large class of non-local PDE's arising from stratified flows

TL;DR

This paper analyzes the spatial behavior of solutions to a broad class of non-local PDEs from stratified flows, establishing decay and growth properties through a theoretical framework.

Contribution

It introduces a general model encompassing many non-local PDEs from stratified flows and studies their spatial decay and growth behaviors.

Findings

Proved sharp pointwise decay properties of solutions.

Established averaged decay estimates.

Identified conditions for solution growth.

Abstract

We propose a theoretical model of a non-local dipersive-dissipative equation which contains as a particular case a large class of non-local PDE's arising from stratified flows. Within this fairly general framework, we study the spatial behavior of solutions proving some sharp pointwise and averaged decay properties as well as some pointwise grow properties.