$L^p-L^q$ estimates on the solutions to $u_{tt}-u_{x_1x_1}=\triangle u_t$

TL;DR

This paper investigates $L^p-L^q$ estimates for solutions to an asymmetric wave equation with dissipation, relevant in magneto-hydrodynamics, employing Green function methods to derive key bounds.

Contribution

It provides new $L^p-L^q$ estimates for a specific asymmetric wave equation with dissipation, advancing understanding in magneto-hydrodynamics models.

Findings

Established $L^p-L^q$ bounds for solutions

Applied Green function techniques effectively

Enhanced theoretical understanding of dissipative wave equations

Abstract

This paper focuses the study on the $L^p-L^q$ estimates on the solutions to an asymmetric wave equation with dissipation which arises in the study for the magneto-hydrodynamics by using the method of Green function.