About local continuity with respect to \(L_2\) initial data for energy solutions of the Navier-Stokes equations

DOI10.1007/s00208-020-02020-6zbMath1489.35179OpenAlexW3038554209MaRDI QIDQ832482

Tobias Barker

Publication date: 25 March 2022

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-020-02020-6

zbMATH Keywords

regularityNavier-Stokes equationsHadamard well-posedness

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Stability in context of PDEs (35B35) Navier-Stokes equations (35Q30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Strong solutions to PDEs (35D35) Harmonic analysis and PDEs (42B37)

Related Items (1)

The continuous dependence for the Navier-Stokes equations in \(\dot{B}^{\frac{d}{p}-1}_{p,r}\)

Cites Work

• Unnamed Item
• Regularity of the Koch-Tataru solutions to Navier-Stokes system
• Hölder continuity for a drift-diffusion equation with pressure
• Minimal initial data for potential Navier-Stokes singularities
• A generalization of a theorem by Kato on Navier-Stokes equations
• On global infinite energy solutions to the Navier-Stokes equations in two dimensions
• Well-chosen weak solutions of the instationary Navier-Stokes system and their uniqueness
• Global weak Besov solutions of the Navier-Stokes equations and applications
• Uniqueness results for weak Leray-Hopf solutions of the Navier-Stokes system with initial values in critical spaces
• Uniqueness for some Leray-Hopf solutions to the Navier-Stokes equations.
• Flows of non-Lipschitzian vector fields and Navier-Stokes equations
• Localized smoothing for the Navier-Stokes equations and concentration of critical norms near singularities
• Are the incompressible 3d Navier-Stokes equations locally ill-posed in the natural energy space?
• On the weak-strong uniqueness of Koch-Tataru's solution for the Navier-Stokes equations
• The Navier-Stokes equations with data in \(bmo^{-1}\)
• Minimal $L^3$-Initial Data for Potential Navier--Stokes Singularities
• The real butterfly effect
• Initial Values for the Navier-Stokes Equations in Spaces with Weights in Time
• Fourier Analysis and Nonlinear Partial Differential Equations
• About weak-strong uniqueness for the 3D incompressible Navier-Stokes system
• Existence of Weak Solutions for the Navier-Stokes Equations with Initial Data in L p
• THE NAVIER-STOKES EQUATIONS WITH INITIAL VALUES IN BESOV SPACES OF TYPE B -1+3/q q, ∞
• On stability of weak Navier–Stokes solutions with largeL^3,∞initial data
• Partial regularity of suitable weak solutions of the navier-stokes equations
• Un théorème de persistance de la régularité en norme d'espaces de Besov pour les solutions de Koch et Tataru des équations de Navier–Stokes dans
• Interpolation, extrapolation, Morrey spaces and local energy control for the Navier–Stokes equations
• Well-posedness for the Navier-Stokes equations

This page was built for publication: About local continuity with respect to \(L_2\) initial data for energy solutions of the Navier-Stokes equations