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

  title={Stationary solution to the Navier-Stokes equations in the scaling invariant Besov space and its regularity},
  author={Kenta Kaneko and Hideo Kozono and Senjo Shimizu},
  journal={Indiana University Mathematics Journal},
We consider the stationary problem of the Navier-Stokes equations in R for n ≥ 3. We show existence, uniqueness and regularity of solutions in the homogeneous Besov space Ḃ −1+np p,q which is the scaling invariant one. As a corollary of our results, a self-similar solution is obtained. For the proof, several bilinear estimates are established. The essential tool is based on the paraproduct formula and the imbedding theorem in homogeneous Besov spaces. Introduction. Let us consider the… 

Well-posedness and ill-posedness of the stationary Navier–Stokes equations in toroidal Besov spaces

We consider the stationary Navier–Stokes equations in the n-dimensional torus for . We show the existence and uniqueness of solutions in homogeneous toroidal Besov spaces with for small external

Ill-posedness for the stationary Navier-Stokes equations in critical Besov spaces

: This paper presents some progress toward an open question which proposed by Tsurumi (Arch. Ration. Mech. Anal. 234:2, 2019): whether or not the stationary Navier-Stokes equations in R d is

Navier–Stokes equations with external forces in time‐weighted Besov spaces

We show existence theorem of global mild solutions with small initial data and external forces in the time‐weighted Besov space which is an invariant space under the change of scaling. The result on

Stationary solutions for the fractional Navier-Stokes-Coriolis system in Fourier-Besov spaces

In this work we prove the existence of stationary solutions for the tridimensional fractional Navier-Stokes-Coriolis in critical Fourier-Besov spaces. We first deal with the non-stationary fractional

Asymptotic stability of stationary Navier–Stokes flow in Besov spaces

We discuss the asymptotic stability of stationary solutions to the incompressible Navier–Stokes equations on the whole space in Besov spaces. A critical estimate for the semigroup generated by the

Existence of the stationary Navier-Stokes flow in $\mathbb{R}^2$ around a radial flow

. We consider the stationary Navier-Stokes equations on the whole plane R 2 . We show that for a given small and smooth external force around a radial flow, there exists a classical solution decaying

Optimality of Serrin type extension criteria to the Navier-Stokes equations

Abstract We prove that a strong solution u to the Navier-Stokes equations on (0, T) can be extended if either u ∈ Lθ(0, T; U˙∞,1/θ,∞−α $\begin{array}{} \displaystyle

Well-Posedness and Ill-Posedness Problems of the Stationary Navier–Stokes Equations in Scaling Invariant Besov Spaces

  • H. Tsurumi
  • Materials Science
    Archive for Rational Mechanics and Analysis
  • 2019
We consider the stationary Navier–Stokes equations in Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}



Strong solutions of the Navier-Stokes equation in Morrey spaces

It is shown that the nonstationary Navier-Stokes equation (NS) in ℝ+×ℝm is well posed in certain Morrey spacesMp,λ (ℝ+×ℝm) (see the text for the definition: in particularMp,0=Lp ifp>1 andM1,0 is the

Ill-posedness of the stationary Navier-Stokes equations in Besov spaces

  • H. Tsurumi
  • Mathematics
    Journal of Mathematical Analysis and Applications
  • 2019

Semilinear heat equations and the navier-stokes equation with distributions in new function spaces as initial data

In this paper the authors consider a specified Cauchy problem for semilinear hear equations on [Re][sup n] and also the Cauchy problem for the Navier-Stokes equation on [Re][sup n] for n[ge]2 of a


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We shall show that every strong solution u(t) of the Navier‐Stokes equations on (0, T) can be continued beyond t > T provided u ∈ $L^{{{2} \over {1 - \alpha}}}$ (0, T; $\dot F^{- \alpha}_{\infty

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On Landau’s solutions of the Navier–Stokes equations

A special class of solutions of the n-dimensional steady-state Navier–Stokes equations is considered. Bibliography: 23 titles.