On the boundedness of the global solution of anisotropic quasi-geostrophic equations in Sobolev space

DOI10.1007/s12215-022-00851-7arXiv2201.08216OpenAlexW4318336621MaRDI QIDQ6183456

Mustapha Amara

Publication date: 4 January 2024

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.08216

zbMATH Keywords

global regularitysurface quasi-geostrophic equationanisotropic dissipation

Mathematics Subject Classification ID

Navier-Stokes equations (35Q30) Initial value problems for nonlinear higher-order PDEs (35G25) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Fractional partial differential equations (35R11)

Cites Work

• Nonexistence of simple hyperbolic blow-up for the quasi-geostrophic equation
• The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations
• Global solution of anisotropic quasi-geostrophic equations in Sobolev space
• Fourier Analysis and Nonlinear Partial Differential Equations
• Dissipative Quasi-Geostrophic Equation: Local Well-posedness, Global Regularity and Similarity Solutions
• Commutator estimates and the euler and navier-stokes equations
• A note on limiting cases of sobolev embeddings and convolution inequalities
• Weakly Differentiable Functions
• Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar
• A simple one‐dimensional model for the three‐dimensional vorticity equation
• On the global regularity for the anisotropic dissipative surface quasi-geostrophic equation
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