On the well-posedness of 2-D incompressible Navier-Stokes equations with variable viscosity in critical spaces

DOI10.1016/j.jde.2016.01.007zbMath1345.35079arXiv1510.08196OpenAlexW2963447063MaRDI QIDQ5963856

Xiaoping Zhai, Huan Xu, Yongsheng Li

Publication date: 26 February 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.08196

zbMATH Keywords

incompressible Navier-Stokes equationsLittlewood-Paley theorylocal well-posednessLagrangian coordiantes

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) A priori estimates in context of PDEs (35B45) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)

Related Items

Global well-posedness for the density-dependent incompressible flow of liquid crystals ⋮ Global solution to the 3-D density-dependent incompressible flow of liquid crystals ⋮ On the well-posedness of 3-D inhomogeneous incompressible Navier-Stokes equations with variable viscosity ⋮ Global small solutions to a special \(2\frac{1}{2}\)-D compressible viscous non-resistive MHD system ⋮ Global solution to the 3-D inhomogeneous incompressible MHD system with discontinuous density ⋮ Exact solutions to Euler equation and Navier-Stokes equation ⋮ Global well-posedness for the 3D viscous nonhomogeneous incompressible magnetohydrodynamic equations

Cites Work

• Unnamed Item
• Unnamed Item
• Global solutions to 2-D inhomogeneous Navier-Stokes system with general velocity
• Well-posedness of 3-D inhomogeneous Navier-Stokes equations with highly oscillatory initial velocity field
• Global well-posedness of incompressible inhomogeneous fluid systems with bounded density or non-Lipschitz velocity
• A Lagrangian approach for the compressible Navier-Stokes equations
• On the well-posedness of the incompressible density-dependent Euler equations in the \(L^p\) framework
• Unique solvability of an initial- and boundary-value problem for viscous incompressible nonhomogeneous fluids
• Regularity results for two-dimensional flows of multiphase viscous fluids
• Linear transport equations with initial values in Sobolev spaces and application to the Navier-Stokes equations
• Global existence results for the incompressible density dependent Navier-Stokes equations in the whole space
• Incompressible flows with piecewise constant density
• On the wellposedness of three-dimensional inhomogeneous Navier-Stokes equations in the critical spaces
• Global solution to the incompressible inhomogeneous Navier-Stokes equations with some large initial data
• Global existence for an inhomogeneous fluid
• The inviscid limit for density-dependent incompressible fluids
• Navier-Stokes equation with variable density and viscosity in critical space
• Local and global well-posedness results for flows of inhomogeneous viscous fluids
• LOCAL THEORY IN CRITICAL SPACES FOR COMPRESSIBLE VISCOUS AND HEAT-CONDUCTIVE GASES
• Global Unique Solvability of Inhomogeneous Navier-Stokes Equations with Bounded Density
• A Lagrangian Approach for the Incompressible Navier-Stokes Equations with Variable Density
• On the decay and stability of global solutions to the 3-D inhomogeneous Navier-Stokes equations
• Fourier Analysis and Nonlinear Partial Differential Equations
• Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
• Density-dependent incompressible viscous fluids in critical spaces
• Well-Posedness in Critical Spaces for Barotropic Viscous Fluids with Truly Not Constant Density