On the Weak Solutions to the 3D Inviscid Quasi-Geostrophic System

Abstract

The purpose of this note is to study the weak solutions to the inviscid quasi-geostrophic system for initial data belonging to Lebesgue spaces. We give a global existence result as well as detail the connections between several different notions of weak solutions. In addition, we give a condition under which the energy of the system is conserved.

Final version published in SIAM Journal on Mathematical Analysis

References in corpus (2)

• Local and global strong solutions for SQG in bounded domains
• Global in Time Classical Solutions to the 3D Quasi-geostrophic System for Large Initial Data

Cited by in corpus (4)

• Non-uniqueness of Weak Solutions to the 3D Quasi-Geostrophic Equations
• Classical Solutions for the 3D Quasi-Geostrophic System on a Bounded Domain
• On the well-posedness of the inviscid multi-layer quasi-geostrophic equations
• The Inviscid 3D Quasi-Geostrophic System on Bounded Domains