On the hydrostatic limit of stably stratified fluids with isopycnal diffusivity

DOI10.1080/03605302.2024.2366226MaRDI QIDQ6595128

Vincent Duchêne, Roberta Bianchini

Publication date: 29 August 2024

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Hydrology, hydrography, oceanography (86A05) Asymptotic methods, singular perturbations applied to problems in fluid mechanics (76M45) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Stratification effects in inviscid fluids (76B70) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Geophysical flows (76U60)

Cites Work

• Unnamed Item
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• Two-velocity hydrodynamics in fluid mechanics. II. Existence of global \(\kappa\)-entropy solutions to the compressible Navier-Stokes systems with degenerate viscosities
• Dissipative measure-valued solutions to the compressible Navier-Stokes system
• Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain
• Some diffusive capillary models of Korteweg type
• Local and global well-posedness of strong solutions to the 3D primitive equations with vertical Eddy diffusivity
• On the hydrostatic approximation of the Navier-Stokes equations in a thin strip
• Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects
• About the barotropic compressible quantum Navier-Stokes equations
• Mathematical justification of a shallow water model
• Ill-posedness of the hydrostatic Euler and Navier-Stokes equations
• Compact sets in the space \(L^ p(0,T;B)\)
• Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model
• Beyond Navier-Stokes
• Semi-implicit staggered mesh scheme for the multi-layer shallow water system
• An explicit asymptotic preserving low Froude scheme for the multilayer shallow water model with density stratification
• The primitive equations as the small aspect ratio limit of the Navier-Stokes equations: rigorous justification of the hydrostatic approximation
• Finite-time blowup and ill-posedness in Sobolev spaces of the inviscid primitive equations with rotation
• Normal mode decomposition and dispersive and nonlinear mixing in stratified fluids
• Global existence of entropy-weak solutions to the compressible Navier-Stokes equations with non-linear density dependent viscosities
• On the \(H ^{s }\) theory of hydrostatic Euler equations
• Finite-time blowup for the inviscid primitive equations of oceanic and atmospheric dynamics
• Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics
• Existence of global weak solutions for 3D degenerate compressible Navier-Stokes equations
• Ill-posedness of the hydrostatic Euler and singular Vlasov equations
• The primitive equations approximation of the anisotropic horizontally viscous \(3D\) Navier-Stokes equations
• Rigorous derivation of the full primitive equations by the scaled Boussinesq equations with rotation
• Mathematical Justification of the Hydrostatic Approximation in the Primitive Equations of Geophysical Fluid Dynamics
• The multilayer shallow water system in the limit of small density contrast
• Fourier Analysis and Nonlinear Partial Differential Equations
• Global Well-Posedness of the Three-Dimensional Primitive Equations with Only Horizontal Viscosity and Diffusion
• A Note on the Existence of Certain Viscous Flows
• On the Barotropic Compressible Navier–Stokes Equations
• Compressible and incompressible fluids
• Incompletely Parabolic Problems in Fluid Dynamics
• Homogeneous hydrostatic flows with convex velocity profiles
• On Some Compressible Fluid Models: Korteweg, Lubrication, and Shallow Water Systems
• On the derivation of homogeneous hydrostatic equations
• Stability of Vortices in Ideal Fluids : the Legacy of Kelvin and Rayleigh
• Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier–Stokes equations*
• Global Weak Solutions to Compressible Navier–Stokes Equations for Quantum Fluids
• Viscous Regularization of the Euler Equations and Entropy Principles
• Blowup of solutions of the hydrostatic Euler equations
• On the stability of heterogeneous shear flows
• Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation
• Analysis of the generalized Aw-Rascle model
• Quantitative convergence rates for scaling limit of SPDEs with transport noise
• On the rigorous mathematical derivation for the viscous primitive equations with density stratification
• Stochastic transport in upper ocean dynamics II, STUOD 2022. Proceedings of the 3rd workshop, London, UK, September 26--29, 2022

Related Items (2)

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