Long-time existence for the 2D ideal Boussinesq and the 2D density-dependent Euler equations

2025/07/24 by Bae, Hantaek, Filho, Milton Lopes, Mazzucato, Anna +1 · 1 citation
#35Q35 #76B03 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.18244

Abstract

We establish long-time existence of smooth solutions to the 2D ideal Boussinesq equations and to the 2D non-homogeneous incompressible Euler equations for initial data consisting of small temperature perturbations, or small density perturbations, of smooth initial flows which are not necessarily small. Both results are known (see Danchin and Fanelli 2013, Danchin 2011 in the references) but the technique we develop to prove them is at the same time elementary and has broad potential applicability.

Citations

• On the well-posedness in Besov-Herz spaces for the inhomogeneous incompressible Euler equations
• Higher Order Regularity and Blow-up Criterion for Semi-dissipative and\n Ideal Boussinesq Equations
• Remarks on the lifespan of the solutions to some models of incompressible fluid mechanics
• On the existence of certain singular integrals
• Local existence and blow-up criterion for the Boussinesq equations

Cited by

• Lifespan of the Non-resistive Hall-MHD System with Small Magnetic Gradient

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