Sobolev regular solutions for the incompressible Navier-Stokes equations in higher dimensions: asymptotics and representation formulae

DOI10.1007/s12215-020-00540-3zbMath1477.35148OpenAlexW3045015959MaRDI QIDQ2047472

Vicenţiu D. Rădulescu, Weiping Yan

Publication date: 20 August 2021

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12215-020-00540-3

zbMATH Keywords

Navier-Stokes equationsNash-Moser iterationCalderon-Zygmund theorySobolev regular solution

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) Navier-Stokes equations for incompressible viscous fluids (76D05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Euler equations (35Q31)

Related Items (1)

Asymptotic stability of explicit blowup solutions for three-dimensional incompressible magnetohydrodynamics equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The motion of closed hypersurfaces in the central force fields
• A class of solutions to stationary Stokes and Navier-Stokes equations with boundary data in \(W^{-1/q,q}\)
• The imbedding problem for Riemannian manifolds
• A rapid convergence method for a singular perturbation problem
• Fine properties of self-similar solutions of the Navier-Stokes equations
• Existence and regularity of very weak solutions of the stationary Navier-Stokes equations
• Mixed boundary value problems for the stationary Navier-Stokes system in polyhedral domains
• Stationary solutions to the Navier-Stokes equations in dimension four
• On Leray's self-similar solutions of the Navier-Stokes equations
• Nonuniqueness of weak solutions to the Navier-Stokes equation
• Existence of regular solutions to the stationary Navier-Stokes equations
• Regular solutions of the stationary Navier-Stokes equations on \(\mathbb{R}^ 5\)
• Existence of standing waves for quasi-linear Schrödinger equations on \(T^n\)
• Regularity criteria for Navier-Stokes equations with slip boundary conditions on non-flat boundaries via two velocity components
• Well/ill-posedness for the dissipative Navier-Stokes system in generalized Carleson measure spaces
• Maximal \(L^{p}-L^{q}\) regularity to the Stokes problem with Navier boundary conditions
• Stationary solutions and nonuniqueness of weak solutions for the Navier-Stokes equations in high dimensions
• Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions
• On the weak solutions to steady Navier-Stokes equations with mixed boundary conditions
• Long time existence for the bosonic membrane in the light cone gauge
• Existence d'ondes de rarefaction pour des systems quasi‐lineaires hyperboliques multidimensionnels
• Existence, uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in ℝ n
• A new proof of the Caffarelli-Kohn-Nirenberg theorem
• Partial regularity of suitable weak solutions of the navier-stokes equations
• Dynamical behavior near explicit self-similar blow–up solutions for the Born–Infeld equation
• Well-posedness for the Navier-Stokes equations

This page was built for publication: Sobolev regular solutions for the incompressible Navier-Stokes equations in higher dimensions: asymptotics and representation formulae