Stationary solution to the Navier-Stokes equations in the scaling invariant Besov space and its regularity

DOI10.1512/iumj.2019.68.7650zbMath1428.35298OpenAlexW2953641355WikidataQ127571730 ScholiaQ127571730MaRDI QIDQ5237501

Hideo Kozono, Kenta Kaneko, Senjo Shimizu

Publication date: 18 October 2019

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/7cac34bc141f4cdcefe9e0a82c4cfdcfc34b92c5

zbMATH Keywords

Navier-Stokes equationsself-similar solutionexistence, uniqueness, and regularity

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Navier-Stokes equations (35Q30) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Self-similar solutions to PDEs (35C06)

Related Items (16)

Ill-posedness of the stationary Navier-Stokes equations in Besov spaces ⋮ Well-posedness of mild solutions for the fractional Navier-Stokes equations in Besov spaces ⋮ Stability of stationary solutions to the Navier–Stokes equations in the Besov space ⋮ The two‐dimensional stationary Navier–Stokes equations in toroidal Besov spaces ⋮ Existence of the stationary Navier-Stokes flow in \(\mathbb{R}^2\) around a radial flow ⋮ Stationary solutions for the fractional Navier-Stokes-Coriolis system in Fourier-Besov spaces ⋮ Counter-examples of the bilinear estimates of the Hölder type inequality in homogeneous Besov spaces ⋮ Strong solutions of the Navier-Stokes equations with singular data ⋮ Optimality of Serrin type extension criteria to the Navier-Stokes equations ⋮ Preface ⋮ Necessary and sufficient condition on initial data in the Besov space for solutions in the Serrin class of the Navier-Stokes equations ⋮ Well-posedness and ill-posedness of the stationary Navier–Stokes equations in toroidal Besov spaces ⋮ Stability of singular solutions to the Navier-Stokes system ⋮ Well-posedness and ill-posedness problems of the stationary Navier-Stokes equations in scaling invariant Besov spaces ⋮ Various regularity estimates for the Keller-Segel-Navier-Stokes system in Besov spaces ⋮ Asymptotic stability of stationary Navier–Stokes flow in Besov spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
• A new proof of the Jawerth--Franke embedding
• Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation
• \(L^ n\) solutions of the stationary and nonstationary Navier-Stokes equations in \(\mathbb{R}^ n\)
• On the stationary and nonstationary Navier-Stokes equations in \(R^ n\)
• Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'hydrodynamique
• Littlewood-Paley decomposition and Navier-Stokes equations
• On Landau's solutions of the Navier-Stokes equations
• On the exterior stationary problem for the Navier-Stokes equations, and associated perturbation problems
• On stationary solutions of the Navier-Stokes equations as limits of nonstationary solutions
• Bilinear estimates in homogeneous Triebel-Lizorkin spaces and the Navier-Stokes equations
• Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
• Some observations on Besov and Lizorkin-Triebel spaces.
• Semilinear heat equations and the navier-stokes equation with distributions in new function spaces as initial data
• NAVIER-STOKES EQUATIONS IN THE BESOV SPACE NEAR L∞ AND BMO
• Self-similar solutions for navier-stokes equations in
• The stability of small stationary solutions in Morrey spaces of the Navier-Stokes equation
• Well-posedness and ill-posedness of the stationary Navier–Stokes equations in toroidal Besov spaces
• Strong solutions of the Navier-Stokes equation in Morrey spaces

This page was built for publication: Stationary solution to the Navier-Stokes equations in the scaling invariant Besov space and its regularity