Local well-posedness of strong solutions to the 2D nonhomogeneous primitive equations with density-dependent viscosity

TL;DR

This paper proves local well-posedness for strong solutions to 2D nonhomogeneous primitive equations with density-dependent viscosity, allowing initial vacuum and providing blow-up criteria for finite-time solutions.

Contribution

It establishes local well-posedness for a class of primitive equations with density-dependent viscosity, including cases with initial vacuum, which was not previously addressed.

Findings

Well-posedness proven under natural compatibility conditions

Initial vacuum is permitted in the analysis

Blow-up criterion for finite-time solutions provided

Abstract

In this paper, we consider the initial-boundary value problem of the nonhomogeneous primitive equations with density-dependent viscosity. Local well-posedness of strong solutions is established for this system with a natural compatibility condition. The initial density does not need to be strictly positive and may contain vacuum. Meanwhile, we also give the corresponding blow-up criterion if the maximum existence interval with respect to the time is finite.