Solutions in mixed-norm Sobolev-Lorentz spaces to the initial value problem for the Navier-Stokes equations

DOI10.1016/j.jmaa.2014.03.068zbMath1308.35166OpenAlexW2038844941MaRDI QIDQ483028

D. Q. Khai, Nguyen Minh Tri

Publication date: 15 December 2014

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.03.068

zbMATH Keywords

Navier-Stokes equationsexistence and uniqueness of mild solutionsmixed-norm Sobolev-Lorentz spaces

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (11)

Gradient estimates in anisotropic Lorentz spaces to general elliptic equations of \(p\)-growth ⋮ Well-posedness for the Navier-Stokes equations with data in homogeneous Sobolev-Lorentz spaces ⋮ Well-posedness for the Navier-Stokes equations with datum in the Sobolev spaces ⋮ Regularity criteria via horizontal component of velocity for the Boussinesq equations in anisotropic Lorentz spaces ⋮ On regularity of weak solutions for the Navier–Stokes equations in general domains ⋮ Regularity criteria for the 3D axisymmetric non-resistive MHD system in the swirl component of the vorticity ⋮ Calderón–Zygmund theory in Lorentz mixed‐norm spaces and its application to compressible fluids ⋮ Regularity criteria for the 3D axisymmetric non-resistive MHD system ⋮ Regularity criteria of the axisymmetric Navier-Stokes equations and Hardy-Sobolev inequality in mixed Lorentz spaces ⋮ Well-posedness for the Navier-Stokes equations with datum in Sobolev-Fourier-Lorentz spaces ⋮ Time decay rates of the \(L^3\)-norm for strong solutions to the Navier-Stokes equations in \(\mathbb{R}^3\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A class of elliptic equations in anisotropic spaces
• An alternative approach to regularity for the Navier-Stokes equations in critical spaces
• On the interior regularity of weak solutions of the Navier-Stokes equations
• The spaces \(L^ p\), with mixed norm
• Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
• Ill-posedness of the Navier-Stokes equations in a critical space in 3D
• Solutions for semilinear parabolic equations in \(L^ p\) and regularity of weak solutions of the Navier-Stokes system
• The resolution of the Navier-Stokes equations in anisotropic spaces
• Navier and Stokes meet the wavelet
• Flows of non-Lipschitzian vector fields and Navier-Stokes equations
• Global large solutions to 3-D inhomogeneous Navier-Stokes system with one slow variable
• On the Navier-Stokes initial value problem. I
• The initial value problem for the Navier-Stokes equations with data in L\(^p\)
• Reduced Sobolev Inequalities
• Analysis on Morrey Spaces and Applications to Navier-Stokes and Other Evolution Equations
• Semilinear heat equations and the navier-stokes equation with distributions in new function spaces as initial data
• A Uniqueness Result for the Navier--Stokes Equations with Vanishing Vertical Viscosity
• Fluids with anisotropic viscosity
• Strong solutions of the Navier-Stokes equation in Morrey spaces
• Well-posedness for the Navier-Stokes equations
• Uniqueness for mild solutions of Navier-Stokes equations in \(L^3(\mathbb{R}^3)\) and other limit functional spaces

This page was built for publication: Solutions in mixed-norm Sobolev-Lorentz spaces to the initial value problem for the Navier-Stokes equations