On the Cauchy problem of a weakly dissipative $\mu$HS equation

TL;DR

This paper investigates the well-posedness, blow-up scenarios, and global existence of solutions for a weakly dissipative $$HS equation using Kato's semigroup theory.

Contribution

It establishes local well-posedness, characterizes blow-up conditions, and provides global existence results for the weakly dissipative $$HS equation, advancing understanding of its solution behavior.

Findings

Established local well-posedness via Kato's theory

Derived precise blow-up scenarios for strong solutions

Presented conditions for global existence of solutions

Abstract

In this paper, we study the Cauchy problem of a weakly dissipative $\mu$HS equation. We first establish the local well-posedness for the weakly dissipative $\mu$HS equation by Kato's semigroup theory. Then, we derive the precise blow-up scenario for strong solutions to the equation. Moreover, we present some blow-up results for strong solutions to the equation. Finally, we give two global existence results to the equation.