Global weak solutions to a weakly dissipative $\mu$HS equation

TL;DR

This paper proves the global existence of weak solutions for a weakly dissipative $$HS equation using approximation methods and Helly's theorem, contributing to the mathematical understanding of such dissipative equations.

Contribution

It introduces a new approach to establish global weak solutions for the weakly dissipative $$HS equation, expanding the theoretical framework for these types of equations.

Findings

Established global existence of weak solutions

Used smooth approximation and Helly's theorem effectively

Contributed to the mathematical theory of dissipative equations

Abstract

This paper is concerned with global existence of weak solutions for a weakly dissipative $\mu$HS equation by using smooth approximate to initial data and Helly$^{,}$s theorem.