On the hydrostatic approximation of the Navier-Stokes equations in a thin strip

DOI10.1016/j.aim.2020.107293zbMath1446.35105arXiv1904.04438OpenAlexW3042435673MaRDI QIDQ783207

Ping Zhang, Zhifei Zhang, Marius Paicu

Publication date: 11 August 2020

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.04438

zbMATH Keywords

incompressible Navier-Stokes equationshydrostatic approximationradius of analyticity

Mathematics Subject Classification ID

Navier-Stokes equations (35Q30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (19)

On the Hydrostatic Approximation of the MHD Equations in a Thin Strip ⋮ Global hydrostatic approximation of the hyperbolic Navier-Stokes system with small Gevrey class 2 data ⋮ On the effect of fast rotation and vertical viscosity on the lifespan of the \(3D\) Primitive equations ⋮ On the hydrostatic approximation of compressible anisotropic Navier-Stokes equations-rigorous justification ⋮ Gevrey-class-3 regularity of the linearised hyperbolic Prandtl system on a strip ⋮ Local martingale solutions and pathwise uniqueness for the three-dimensional stochastic inviscid primitive equations ⋮ On the role of the displacement current and the Cattaneo's law on boundary layers of plasma ⋮ Improved well-posedness for the triple-deck and related models via concavity ⋮ Higher-order error estimates for physics-informed neural networks approximating the primitive equations ⋮ On the global small solution of 2-D Prandtl system with initial data in the optimal Gevrey class ⋮ Quantitative aspects on the ill-posedness of the Prandtl and hyperbolic Prandtl equations ⋮ 3D Hyperbolic Navier-Stokes Equations in a Thin Strip: Global Well-Posedness and Hydrostatic Limit in Gevrey Space ⋮ Hydrostatic limit of the Navier-Stokes-alpha model ⋮ On the hydrostatic Navier-Stokes equations with Gevrey class 2 data ⋮ Vanishing viscosity limit of the 3D incompressible Oldroyd-B model ⋮ Global existence and the decay of solutions to the Prandtl system with small analytic data ⋮ Local well-posedness of solutions to the boundary layer equations for compressible two-fluid flow ⋮ Hydrostatic approximation of the 2D MHD system in a thin strip with a small analytic data ⋮ Global well-posedness of a Prandtl model from MHD in Gevrey function spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Almost global existence for the Prandtl boundary layer equations
• Zero viscosity limit for analytic solutions of the primitive equations
• Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain
• Global regularity for the Navier-Stokes equations with some classes of large initial data
• Global regularity for some classes of large solutions to the Navier-Stokes equations
• Global solutions to the 3-D incompressible anisotropic Navier-Stokes system in the critical spaces
• Gevrey class regularity for the solutions of the Navier-Stokes equations
• Ill-posedness of the hydrostatic Euler and Navier-Stokes equations
• Zero viscosity limit for analytic solutions, of the Navier-Stokes equation on a half-space. I: Existence for Euler and Prandtl equations
• Well-posedness of the hydrostatic Navier-Stokes equations
• Controllability of the Navier-Stokes equation in a rectangle with a little help of a distributed phantom force
• On the global wellposedness to the 3-D incompressible anisotropic Navier-Stokes equations
• Anisotropic Navier-Stokes equation in critical spaces
• Well-posedness for the Prandtl system without analyticity or monotonicity
• Fourier Analysis and Nonlinear Partial Differential Equations
• On the ill-posedness of the Prandtl equation
• Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
• Some estimates for the anisotropic Navier-Stokes equations and for the hydrostatic approximation
• Well-Posedness of the Boundary Layer Equations
• Global well-posedness for 3D Navier–Stokes equations with ill-prepared initial data
• Long time well-posedness of Prandtl system with small and analytic initial data

This page was built for publication: On the hydrostatic approximation of the Navier-Stokes equations in a thin strip