The 2D Euler-Boussinesq equations in planar polygonal domains with Yudovich's type data

2014/05/12 by Aimin Huang, Huang, Aimin
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1405.2631

openalex publication_date 2014/05/12 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We address the well-posedness of the 2D (Euler)-Boussinesq equations with zero viscosity and positive diffusivity in the polygonal-like domains with Yudovich's type data, which gives a positive answer to part of the questions raised in 2011 [Lai-Pan-Zhao, Initial boundary value problem for two-dimensional viscous Boussinesq equations, Arch. Ration. Mech. Anal. 199 (2011), no. 3, 739-760]. Our analysis on the the polygonal-like domains essentially relies on the recent elliptic regularity results for such domains proved in 2013 [Bardos-Plinio-Temam, The Euler equations in planar nonsmooth convex domains, J. Math. Anal. Appl. 407 (2013), no. 1, 69-89.] and [Plinio-Temam, Grisvard's shift theorem near l^∞ and yudovich theory on polygonal domains, arXiv:1310.5444]

Citations

• Global Well-Posedness Issues for the Inviscid Boussinesq System with Yudovich’s Type Data
• Global regularity for the 2D Boussinesq equations with partial viscosity terms

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