Existence and regularity of weak solutions to the quasi-geostrophic equations in the spaces \(L^p\) or \(\dot{H}^{-1/2}\)

From MaRDI portal
Publication:2466842

DOI10.1007/s00220-007-0356-6zbMath1134.35025OpenAlexW2020628192MaRDI QIDQ2466842

Fabien Marchand

Publication date: 16 January 2008

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

Full work available at URL: https://doi.org/10.1007/s00220-007-0356-6



Lua error in Module:PublicationMSCList at line 37: attempt to index local 'msc_result' (a nil value).


Related Items (52)

The point vortex model for the Euler equationOn the global classical solutions for the generalized SQG equationActive vector models generalising 3D Euler and electron–MHD equationsVelocity statistics for point vortices in the localα-models of turbulenceGlobal existence for the critical dissipative surface quasi-geostrophic equationInviscid Limit for SQG in Bounded DomainsNon existence and strong ill-posedness in \(C^k\) and Sobolev spaces for SQGRegularized and approximate equations for sharp fronts in the surface quasi-geostrophic equation and its generalizationsGlobal solutions of a surface quasigeostrophic front equationPoint vortices for inviscid generalized surface quasi-geostrophic modelsExistence of solutions to fluid equations in Hölder and uniformly local Sobolev spacesEmergence of time periodic solutions for the generalized surface quasi-geostrophic equation in the discKármán vortex street for the generalized surface quasi-geostrophic equationWell-posedness for SQG sharp fronts with unbounded curvatureGlobal solutions for the generalized SQG patch equationStrong ill-posedness for SQG in critical Sobolev spacesNew numerical results for the surface quasi-geostrophic equationOptimal Gevrey regularity for supercritical quasi-geostrophic equationsOn the existence of stationary patchesA scaling limit for the stochastic mSQG equations with multiplicative transport noisesGlobal existence for some transport equations with nonlocal velocityAbsence of anomalous dissipation of energy in forced two dimensional fluid equationsGlobal Smooth Solutions for the Inviscid SQG EquationNonuniqueness of Weak Solutions to the 3 Dimensional Quasi-Geostrophic EquationsWeak-strong uniqueness criteria for the critical quasi-geostrophic equationGlobal and local existence for the dissipative critical SQG equation with small oscillationsMartingale solutions for stochastic active scalar equations perturbed by non-trace class noiseLong time dynamics of forced critical SQGRemark on the absolute value in Sobolev spacesLimit theorems and fluctuations for point vortices of generalized Euler equationsInviscid models generalizing the two-dimensional Euler and the surface quasi-geostrophic equationsRegularity results for a class of generalized surface quasi-geostrophic equationsmSQG equations in distributional spaces and point vortex approximation2D quasi-geostrophic equation; sub-critical and critical casesInvariant measures and global well posedness for the SQG equationJustification of the Point Vortex Approximation for Modified Surface Quasi-Geostrophic EquationsA priori estimates for the 3D quasi-geostrophic systemExistence and regularity of co-rotating and traveling-wave vortex solutions for the generalized SQG equationThe lifespan of classical solutions for the inviscid surface quasi-geostrophic equationThe inviscid three dimensional quasi-geostrophic system on bounded domainsNon-uniqueness of steady-state weak solutions to the surface quasi-geostrophic equationsOn the Weak Solutions to the Three-Dimensional Inviscid Quasi-Geostrophic SystemUpper and lower bounds of decay rates for \(\dot{H}^{- \frac{1}{2}}\) weak solutions of the surface quasi-geostrophic equationComputer-assisted proofs in PDE: a surveyA direct approach to nonuniqueness and failure of compactness for the SQG equationGlobal well-posedness, Gevrey class regularity and large time asymptotics for the dissipative quasi-geostrophic equation in Fourier-Besov spacesStatistical measures and selective decay principle for generalized Euler dynamics: formulation and application to the formation of strong frontsOn white noise solutions of mSQG equations on \(\mathbb{R}^2\)Non-decaying solutions to the critical surface quasi-geostrophic equations with symmetriesClassical solutions for the 3D quasi-geostrophic system on a bounded domainGlobal solutions for the generalized SQG equation and rearrangementsHigh Order Conservative Finite Difference/Fourier Spectral Methods for Inviscid Surface Quasi-Geostrophic Flows



Cites Work


This page was built for publication: Existence and regularity of weak solutions to the quasi-geostrophic equations in the spaces \(L^p\) or \(\dot{H}^{-1/2}\)