Global in time classical solutions to the 3D quasi-geostrophic system for large initial data

DOI10.1007/s00220-017-3049-9zbMath1417.35137arXiv1610.04764OpenAlexW2533734657MaRDI QIDQ1709806

Alexis F. Vasseur, Matthew D. Novack

Publication date: 6 April 2018

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.04764

zbMATH Keywords

bootstrapping3D quasi-geostrophic systemBeale-Kato-Majda techniquesDe-Giorgi regularization effect

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Hydrology, hydrography, oceanography (86A05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs in connection with geophysics (35Q86)

Related Items (7)

On the well-posedness of the inviscid multi-layer quasi-geostrophic equations ⋮ Energy-conserving Galerkin approximations for quasigeostrophic dynamics ⋮ Nonuniqueness of Weak Solutions to the 3 Dimensional Quasi-Geostrophic Equations ⋮ Hölder regularity up to the boundary for critical SQG on bounded domains ⋮ The inviscid three dimensional quasi-geostrophic system on bounded domains ⋮ On the Weak Solutions to the Three-Dimensional Inviscid Quasi-Geostrophic System ⋮ Classical solutions for the 3D quasi-geostrophic system on a bounded domain

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Regularity for parabolic integro-differential equations with very irregular kernels
• Hitchhiker's guide to the fractional Sobolev spaces
• Global weak solutions to the inviscid 3D quasi-geostrophic equation
• Global well-posedness for an advection-diffusion equation arising in magneto-geostrophic dynamics
• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation
• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• Regularity criteria for the dissipative quasi-geostrophic equations in Hölder spaces
• Remarks on the breakdown of smooth solutions for the 3-D Euler equations
• Lifting in Sobolev spaces
• A maximum principle applied to quasi-geostrophic equations
• Nonlinear maximum principles for dissipative linear nonlocal operators and applications
• Derivation of quasi-geostrophic potential vorticity equations
• Variation on a theme of Caffarelli and Vasseur
• Regularity theory for parabolic nonlinear integral operators
• Fourier Analysis and Nonlinear Partial Differential Equations
• Modern Fourier Analysis
• Euler Equations, Navier-Stokes Equations and Turbulence
• Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids
• Validity of the Quasigeostrophic Model for Large-Scale Flow in the Atmosphere and Ocean
• Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar
• Surface quasi-geostrophic dynamics

This page was built for publication: Global in time classical solutions to the 3D quasi-geostrophic system for large initial data