Hasegawa-Mima equation in bounded domain with singular density

2025/09/20 by Franco Flandoli, Flandoli, Franco, Yassine Tahraoui +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2509.16754

openalex publication_date 2025/09/20 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

We investigate the well-posedness of Hasegawa-Mima equation (HME) in bounded domain with Dirichlet boundary condition and singular density under different regularity assumptions on the data. Our approach relies on the coupling of a fourth-order regularization of the HME, the spectral Galerkin method and an appropriate regularization of the singular density. Uniqueness holds in the class of solutions with very mild singularities à la Yudovich or with bounded densities.

Citations

• An elementary proof of existence and uniqueness for the Euler flow in localized Yudovich spaces
• Nonuniqueness of solutions to the Euler equations with vorticity in a Lorentz space
• Spectral Theory of Partial Differential Equations - Lecture Notes

Related

• A uniform estimate for an equation with Holderian condition and boundary singularity
• Analysis and boundary value problems on singular domains: an approach via bounded geometry
• Boundary behavior for a singular quasi-linear elliptic equation
• Boundary regularity theory of the singular Lane-Emden-Fowler equation in a Lipschitz domain
• Isolated Singularities of Solutions to the Yamabe Equation with boundary in Dimension 3 and 4