Long-time solvability for the 2D dispersive SQG equation with improved regularity

Vladimir Angulo-Castillo; Lucas C. F. Ferreira; Leonardo Kosloff

doi:10.3934/dcds.2020082

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2020, Volume 40, Issue 3: 1411-1433. Doi: 10.3934/dcds.2020082

This issue Previous Article Existence of periodically invariant tori on resonant surfaces for twist mappings Next Article On global axisymmetric solutions to 2D compressible full Euler equations of Chaplygin gases

Long-time solvability for the 2D dispersive SQG equation with improved regularity

1.
Departamento de Matemáticas, Universidad Nacional de Colombia - Sede Orinoquia, Kilometro 9 vía a Caño Limón, Arauca, Colombia
2.
IMECC-Departamento de Matemática, Universidade Estadual de Campinas, Rua Sérgio Buarque de Holanda, CEP 13083-859, Campinas, SP, Brazil

^* Corresponding author: Lucas C. F. Ferreira
^* Corresponding author: Lucas C. F. Ferreira

Received: December 31, 2018

Revised: June 30, 2019

Published: December 2019

The first author was supported by CNPq, Brazil. The second author was supported by FAPESP and CNPq, Brazil. The third author was supported by FAPESP, Brazil

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Abstract

In this paper, we study the long-time existence and uniqueness (solvability) for the initial value problem of the 2D inviscid dispersive SQG equation. First we obtain the local solvability with existence-time independent of the amplitude parameter $ A $. Then, assuming more regularity and using a blow-up criterion of BKM type and a space-time estimate of Strichartz type, we prove long-time solvability of solutions in Besov spaces for large $ A $ and arbitrary initial data. In comparison with previous results, we are able to consider improved cases of the regularity and larger initial data classes.

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Mathematics Subject Classification: Primary: 76U05, 46E35, 35Q35; Secondary: 76B03, 35A01.

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