Well-posedness and ill-posedness problems of the stationary Navier-Stokes equations in scaling invariant Besov spaces

DOI10.1007/s00205-019-01404-6zbMath1428.35315OpenAlexW2961035737MaRDI QIDQ2322733

Hiroyuki Tsurumi

Publication date: 5 September 2019

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00205-019-01404-6

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Spaces of vector- and operator-valued functions (46E40) Ill-posed problems for PDEs (35R25) Navier-Stokes equations (35Q30)

Related Items (7)

Ill-posedness of a multidimensional chemotaxis system in the critical Besov spaces ⋮ Ill-posedness issue on a multidimensional chemotaxis equations in the critical 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 ⋮ Counter-examples of the bilinear estimates of the Hölder type inequality in homogeneous Besov spaces ⋮ Stability of singular solutions to the Navier-Stokes system ⋮ Asymptotic stability of stationary Navier–Stokes flow in Besov spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Stationary Navier-Stokes equations with critically singular external forces: existence and stability results
• Sharp well-posedness and ill-posedness results for a quadratic nonlinear Schrödinger equation
• Ill-posedness of the 3D-Navier-Stokes equations in a generalized Besov space near \(\mathrm{BMO}^{-1}\)
• Ill-posedness of the Navier-Stokes equations in a critical space in 3D
• 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
• On stationary solutions of the Navier-Stokes equations as limits of nonstationary solutions
• L^p-Solutions of the Steady-State Navier–Stokes Equations with Rough External Forces
• Modern Fourier Analysis
• Stationary solution to the Navier-Stokes equations in the scaling invariant Besov space and its regularity

This page was built for publication: Well-posedness and ill-posedness problems of the stationary Navier-Stokes equations in scaling invariant Besov spaces