Existence, Uniqueness, and Smoothing for Generalized EMHD

TL;DR

This paper investigates the mathematical properties of generalized EMHD equations, proving local and global existence, uniqueness, smoothing effects, and decay rates of solutions in Sobolev spaces.

Contribution

It establishes the first comprehensive analysis of existence, uniqueness, smoothing, and decay for generalized EMHD equations, including small data global results.

Findings

Local existence and uniqueness in critical Sobolev spaces

Global existence and uniqueness for small initial data

Solutions exhibit instantaneous smoothing and decay over time

Abstract

We study the Cauchy problem for generalized electron magnetohydrodynamics (EMHD). We establish the local existence and uniqueness of solutions in critical Sobolev spaces, as well as global existence and uniqueness for small initial data. In addition, we prove an instantaneous smoothing effect for the corresponding solutions. Finally, we derive time decay rates for the global solutions.