Global generalized solutions for Maxwell-alpha and Euler-alpha equations

TL;DR

This paper establishes the existence of global dissipative solutions for the Maxwell-alpha and Euler-alpha equations, extending the mathematical understanding of these fluid models in both 2D and 3D.

Contribution

It introduces a framework for proving the existence of global solutions for Maxwell-alpha and Euler-alpha models, including a novel abstract Hilbert space approach.

Findings

Existence of global dissipative solutions in 2D and 3D.

Development of an abstract Hilbert space framework for dissipative solutions.

Application to corotational Maxwell and inviscid fluids equations.

Abstract

We study initial-boundary value problems for the Lagrangian averaged alpha models for the equations of motion for the corotational Maxwell and inviscid fluids in 2D and 3D. We show existence of (global in time) dissipative solutions to these problems. We also discuss the idea of dissipative solution in an abstract Hilbert space framework.