Long-Time Existence of Smooth Solutions for the Rapidly Rotating Shallow-Water and Euler Equations

DOI10.1137/070693643zbMath1152.76054arXiv0706.0758OpenAlexW2115785978MaRDI QIDQ3525975

Bin Cheng, Eitan Tadmor

Publication date: 23 September 2008

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0706.0758

zbMATH Keywords

critical thresholdperiodic-in-time approximate solutionpressureless equations

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Hydrology, hydrography, oceanography (86A05) General theory of rotating fluids (76U05) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Rotation in hydrodynamic stability (76E07) Stability and instability of geophysical and astrophysical flows (76E20)

Related Items (16)

Existence of Global Classical Solutions for the Saint-Venant Equations ⋮ Singularity formation for rotational gas dynamics ⋮ Global smooth solutions to the two dimensional compressible Euler equations with the rotational Coriolis forcing ⋮ Singularity for the one-dimensional rotating Euler equations of Chaplygin gases ⋮ On the classical solutions of two dimensional inviscid rotating shallow water system ⋮ Analytical properties for a stochastic rotating shallow water model under location uncertainty ⋮ An initial-boundary value problem for the one-dimensional rotating shallow water magnetohydrodynamic equations ⋮ Blowup for projected 2-dimensional \(C^2\) solutions of compressible Euler equations with Coriolis force ⋮ On properties of solutions of the Cauchy problem for two-dimensional transport equations on a rotating plane ⋮ Singularity Formation and Global Existence of Classical Solutions for One-Dimensional Rotating Shallow Water System ⋮ Global regularity of two-dimensional flocking hydrodynamics ⋮ Global regularity of the 4D restricted Euler equations ⋮ Critical thresholds in hyperbolic relaxation systems ⋮ Cauchy problem for viscous rotating shallow water equations ⋮ Well-posedness for the viscous rotating shallow water equations with friction terms ⋮ Formation of singularity for the classical solutions of the rotating shallow water system

This page was built for publication: Long-Time Existence of Smooth Solutions for the Rapidly Rotating Shallow-Water and Euler Equations