On the global well-posedness of one-dimensional fluid models with nonlocal velocity

Zhuan Ye

Vol. 304 (2020), No. 2, 713–752

DOI: 10.2140/pjm.2020.304.713

Abstract

In this paper, we consider one-dimensional fluid models with nonlocal velocity, and establish the global well-posedness of classical solutions to such models with large initial data in suitable Sobolev spaces.

Keywords

one-dimensional equation, nonlocal velocity, global well-posedness

Mathematical Subject Classification 2010

Primary: 35B65, 35Q35, 76D03

Milestones

Received: 2 November 2018

Revised: 28 May 2019

Accepted: 29 August 2019

Published: 12 February 2020