On the existence of stationary patches
Javier G\'omez-Serrano
TL;DR
This paper proves the existence of a family of analytic stationary patch solutions for the SQG and gSQG equations, addressing an open problem in mathematical fluid dynamics.
Contribution
It establishes the existence of stationary patch solutions for SQG and gSQG equations, advancing understanding of their mathematical structure.
Findings
Existence of analytic stationary patch solutions confirmed.
Addresses an open problem from previous research.
Contributes to the theoretical understanding of SQG and gSQG equations.
Abstract
In this paper, we show the existence of a family of analytic stationary patch solutions of the SQG and gSQG equations. This answers an open problem in [F. de la Hoz, Z. Hassainia, T. Hmidi. Arch. Ration. Mech. Anal., 220(3):1209-1281, 2016].
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