Global weak solutions for SQG in bounded domains
Peter Constantin, Huy Quang Nguyen
TL;DR
This paper establishes the existence of global weak solutions in the $L^2$ space for the inviscid surface quasi-geostrophic (SQG) equation within bounded domains, advancing mathematical understanding of this fluid dynamics model.
Contribution
It proves the existence of global weak solutions for the inviscid SQG equation specifically in bounded domains, which was previously unresolved.
Findings
Existence of global weak $L^2$ solutions proven.
Solutions are valid in bounded domain settings.
Mathematical framework for SQG in bounded domains developed.
Abstract
We prove existence of global weak solutions of the inviscid SQG equation in bounded domains.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Navier-Stokes equation solutions · Stability and Controllability of Differential Equations