The 2D Euler–Boussinesq Equations in Planar Polygonal Domains with Yudovich’s Type Data

Aimin Huang

doi:10.1007/s40304-015-0045-2

Communications in Mathematics and Statistics ›› 2014, Vol. 2 ›› Issue (3-4) : 369 -391. DOI: 10.1007/s40304-015-0045-2

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The 2D Euler–Boussinesq Equations in Planar Polygonal Domains with Yudovich’s Type Data

Aimin Huang ¹^,^a

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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 Lai (Arch Ration Mech Anal 199(3):739–760, 2011). Our analysis on the the polygonal-like domains essentially relies on the recent elliptic regularity results for such domains proved in Bardos et al. (J Math Anal Appl 407(1):69–89, 2013) and Di Plinio (SIAM J Math Anal 47(1):159–178, 2015).

Keywords

Boussinesq system / Euler equations / Existence and uniqueness / Yudovich’s type data / Initial-boundary value problem

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Aimin Huang. The 2D Euler–Boussinesq Equations in Planar Polygonal Domains with Yudovich’s Type Data. Communications in Mathematics and Statistics, 2014, 2(3-4): 369-391 DOI:10.1007/s40304-015-0045-2