Stokes and Navier-Stokes problems in a half-space: the existence and uniqueness of solutions a priori nonconvergent to a limit at infinity

DOI10.1007/s10958-009-9458-3zbMath1236.35109OpenAlexW2020695772MaRDI QIDQ1037183

Paolo Maremonti

Publication date: 13 November 2009

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-009-9458-3

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (18)

Navier wall law for nonstationary viscous incompressible flows ⋮ Pointwise decay estimate of Navier-Stokes flows in the half space with slowly decreasing initial value ⋮ On the \(L^p\) Helmholtz decomposition: a review of a result due to Solonnikov ⋮ Global existence of solutions to 2-D Navier-Stokes flow with non-decaying initial data in half-plane ⋮ On the Stokes problem in exterior domains: the maximum modulus theorem ⋮ Non-decaying solutions to the Navier Stokes equations in exterior domains ⋮ The Navier-Stokes flow around the linearly growing steady state with bounded disturbance ⋮ Unnamed Item ⋮ Initial and boundary value problem of the unsteady Navier-Stokes system in the half-space with Hölder continuous boundary data ⋮ Global existence of weak solutions to 3D Navier-Stokes IBVP with non-decaying initial data in exterior domains ⋮ Notes on the space-time decay rate of the Stokes flows in the half space ⋮ Solvability for Stokes system in Hölder spaces in bounded domains and its applications ⋮ Spatial and temporal decay estimate of the Stokes flow of weighted \(L^1\) initial data in the half space ⋮ Continuous alignment of vorticity direction prevents the blow-up of the Navier-Stokes flow under the no-slip boundary condition ⋮ Global existence of solutions to 2-D Navier-Stokes flow with non-decaying initial data in exterior domains ⋮ On the uniqueness of bounded very weak solutions to the Navier–Stokes Cauchy problem ⋮ Conditional stability and periodicity of solutions to evolution equations ⋮ Weighted \(L^q-L^1\) estimate of the Stokes flow in the half space

Cites Work

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• Su un problema esterno relativo alle equazioni di Navier-Stokes
• Nonstationary Stokes equations in a half-space with continuous initial data
• On estimates of solutions of the non-stationary Stokes problem in anisotropic Sobolev spaces and on estimates for the resolvent of the Stokes operator
• A Note on the Cauchy Problem for the Navier–Stokes Equations
• \(L^p\)-theory of the Stokes equation in a half space

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