Well-posedness for the Boussinesq system in critical spaces via maximal regularity

DOI10.5802/aif.3523zbMath1515.35203arXiv2012.02450OpenAlexW3110035863MaRDI QIDQ6040259

Lorenzo Brandolese, Sylvie Monniaux

Publication date: 24 May 2023

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.02450

zbMATH Keywords

existenceuniquenessBoussinesq systemmaximal regularitycritical space

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Free convection (76R10) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

• Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
• The Navier-Stokes equations in nonendpoint borderline Lorentz spaces
• Existence and uniqueness results for the Boussinesq system with data in Lorentz spaces
• On the closedness of the sum of two closed operators
• Uniqueness theorems for the Boussinesq system
• A profile decomposition approach to the \(L^\infty _t(L^{3}_x)\) Navier-Stokes regularity criterion
• Un'applicazione della teoria degli integrali singolari allo studio delle equazioni differenziali lineari astratte del primo ordine
• Fourier Analysis and Nonlinear Partial Differential Equations
• Les théorèmes de Leray et de Fujita-Kato pour le système de Boussinesq partiellement visqueux
• Uniqueness of mild solutions of the Navier-Stokes equation and maximal Lp-regularity
• Heat kernels and maximal l^p—l^qestimates for parabolic evolution equations
• L_3,∞-solutions of the Navier-Stokes equations and backward uniqueness
• Self-similarity in viscous Boussinesq equations
• Uniqueness for mild solutions of Navier-Stokes equations in \(L^3(\mathbb{R}^3)\) and other limit functional spaces
• Maximal regularity and kernel bounds: observations on a theorem by Hieber and Prüss
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