Global solutions to the 3-D incompressible anisotropic Navier-Stokes system in the critical spaces

DOI10.1007/s00220-011-1350-6zbMath1237.35129OpenAlexW2084595004MaRDI QIDQ647377

Ping Zhang, Marius Paicu

Publication date: 23 November 2011

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

Full work available at URL: https://doi.org/10.1007/s00220-011-1350-6

zbMATH Keywords

Navier-Stokes equations3D incompressible anisotropic equationscritical Besov-Sobolev spaces

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Navier-Stokes equations (35Q30) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global solutions to the 3-D incompressible inhomogeneous Navier-Stokes system
• Global wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations in an anisotropic space
• Erratum to: Global wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations in an anisotropic space
• Asymptotic behavior of global solutions to the Navier-Stokes equations in \(\mathbb{R}^3\)
• The resolution of the Navier-Stokes equations in anisotropic spaces
• Uniqueness theorems for the three dimensional Navier-Stokes system
• A generalization of a theorem by Kato on Navier-Stokes equations
• Flows of non-Lipschitzian vector fields and Navier-Stokes equations
• On the Navier-Stokes initial value problem. I
• On the global wellposedness to the 3-D incompressible anisotropic Navier-Stokes equations
• Anisotropic Navier-Stokes equation in critical spaces
• Stability to the global large solutions of 3-D Navier-Stokes equations
• Fourier Analysis and Nonlinear Partial Differential Equations
• Large, global solutions to the Navier-Stokes equations, slowly varying in one direction
• Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
• Ekman layers of rotating fluids, the case of well prepared initial data
• A Uniqueness Result for the Navier--Stokes Equations with Vanishing Vertical Viscosity
• Fluids with anisotropic viscosity
• One component regularity for the Navier–Stokes equations
• Well-posedness for the Navier-Stokes equations

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