The evolution Navier-Stokes equations in a cube under Navier boundary conditions: rarefaction and uniqueness of global solutions

DOI10.1007/s00526-023-02553-zzbMath1529.35331OpenAlexW4386000735MaRDI QIDQ6137576

Gazzola, Filippo, Alessio Falocchi

Publication date: 4 September 2023

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-023-02553-z

zbMATH Keywords

Navier-Stokes equationsNavier boundary conditionsStokes eigenvalue problem

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Navier-Stokes equations for incompressible viscous fluids (76D05) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Navier-Stokes equations (35Q30) Eigenvalue problems for linear operators (47A75) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stokes and Navier-Stokes equations with Navier boundary condition
• Viscous boundary layers for the Navier-Stokes equations with the Navier slip conditions
• On the existence of hydrodynamic motion in a domain with free boundary type conditions
• On the spectrum of the Stokes operator
• Stokes eigenmodes in cubic domain: primitive variable and lattice Boltzmann formulations
• An elementary approach to the 3D Navier-Stokes equations with Navier boundary conditions: existence and uniqueness of various classes of solutions in the flat boundary case
• Eigenvalues of the Stokes operator versus the Dirichlet Laplacian in the plane
• On the hydrodynamic motion in a domain with mixed boundary conditions: Existence, uniqueness, stability and linearization principle
• The Navier-Stokes equations theory and numerical methods. Proceedings of a conference held at Oberwolfach, FRG, Sept. 18-24, 1988
• On a boundary value problem for a stationary system of Navier-Stokes equations
• Valeurs propres d'opérateurs définis par la restriction de systèmes variationnels à des sous-espaces
• Spectrally accurate Stokes eigen-modes on isosceles triangles
• Uniqueness and bifurcation branches for planar steady Navier-Stokes equations under Navier boundary conditions
• Regularity for the 3D evolution Navier-Stokes equations under Navier boundary conditions in some Lipschitz domains
• Remarks on the 3D Stokes eigenvalue problem under Navier boundary conditions
• \(L^p\)-theory for Stokes and Navier-Stokes equations with Navier boundary condition
• Regularity for Stokes and generalized Stokes systems under nonhomogeneous slip-type boundary conditions
• Multidimensional lower bounds for the eigenvalues of Stokes and Dirichlet Laplacian operators
• On the vanishing viscosity limit for the 2D incompressible Navier-Stokes equations with the friction type boundary conditions
• The Eigenfunctions of the Stokes Operator in Special Domains. I
• The Eigenfunctions of the Stokes Operator in Special Domains. II
• The 3D navier-stokes equations seen as a perturbation of the 2D navier-stokes equations
• The Eigenfunctions of the Stokes Operator in Special Domains. III
• APPROXIMATION OF THE LARGER EDDIES IN FLUID MOTIONS II: A MODEL FOR SPACE-FILTERED FLOW
• Global regularity for solutions of the three dimensional Navier–Stokes equation with almost two dimensional initial data