Local in time existence of solution of the Navier-Stokes equations with various types of boundary conditions

DOI10.1007/s41808-021-00109-wzbMath1479.35601OpenAlexW3187311661MaRDI QIDQ2061629

Petra Vacková, Michal Beneš, Petr Kučera

Publication date: 16 December 2021

Published in: Journal of Elliptic and Parabolic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s41808-021-00109-w

zbMATH Keywords

Navier-Stokes equationsmixed boundary conditionsNavier's boundary conditionsdo-nothing boundary conditionslocal in time existence of solutions

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) Stability and instability of nonparallel flows in hydrodynamic stability (76E09) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (1)

On buoyancy‐driven viscous incompressible flows with various types of boundary conditions

Cites Work

• Basic properties of solution of the non-steady Navier-Stokes equations with mixed boundary conditions in a bounded domain
• The Boussinesq system with mixed non-smooth boundary conditions and do-nothing boundary flow
• A steady flow through a plane cascade of profiles with an arbitrarily large inflow -- the mathematical model, existence of a weak solution
• Local solutions to the Navier-Stokes equations with mixed boundary conditions
• A weak solvability of a steady variational inequality of the Navier-Stokes type with mixed boundary conditions.
• The analysis of stationary viscous incompressible flow through a rotating radial blade machine, existence of a weak solution
• On existence and uniqueness of solutions to a Boussinesq system with nonlinear and mixed boundary conditions
• Mixed initial-boundary value problem for the three-dimensional Navier-Stokes equations in polyhedral domains
• Solutions to the Navier-Stokes equations with mixed boundary conditions in two-dimensional bounded domains
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