Global well-posedness for the 2D Euler-Boussinesq-B\rm\acuteenard equations with critical dissipation

2023/06/19 by Zhuan Ye, Ye, Zhuan
Mathematics · #35B65 #35Q35 #35R11 #76B03 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2306.10670

openalex publication_date 2023/06/19 · openalex created_date 2023/06/22 · openalex updated_date 2026/07/28

Abstract

This present paper is dedicated to the study of the Cauchy problem of the two-dimensional Euler-Boussinesq-B\rm\acuteenard equations which couple the incompressible Euler equations for the velocity and a transport equation with critical dissipation for the temperature. We show that there is a global unique solution to this model with Yudovich's type data. This settles the global regularity problem which was remarked by Wu and Xue (J. Differential Equations 253:100--125, 2012).

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