Global Existence of Strong Solutions and Serrin-Type Blowup Criterion for 3D Combustion Model in Bounded Domains

TL;DR

This paper proves the global existence of strong solutions and establishes a blowup criterion for the 3D combustion model in bounded domains, advancing understanding of solution behavior under specific initial conditions.

Contribution

It provides the first rigorous proof of global strong solutions and a Serrin-type blowup criterion for the 3D combustion system in bounded domains.

Findings

Global existence and uniqueness of strong solutions under small initial velocity gradient

A priori bounds for density and velocity fields

Blowup criterion for the 3D combustion system

Abstract

The combustion model is studied in three-dimensional (3D) smooth bounded domains with various types of boundary conditions. The global existence and uniqueness of strong solutions are obtained under the smallness of the gradient of initial velocity in some precise sense. Using the energy method with the estimates of boundary integrals, we obtain the a priori bounds of the density and velocity field. Finally, we establish the blowup criterion for the 3D combustion system.