Sign-changing bubble tower solutions for sinh-Poisson type equations on pierced domains

2023/01/04 by Pablo Figueroa, Figueroa, Pablo
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2301.01845

Abstract

For asymmetric sinh-Poisson type problems with Dirichlet boundary condition arising as a mean field equation of equilibrium turbulence vortices with variable intensities of interest in hydrodynamic turbulence, we address the existence of sign-changing bubble tower solutions on a pierced domain Ω_ε:=Ω∖ B(ξ,ε), where Ω is a smooth bounded domain in ℝ² and B(ξ,ε) is a ball centered at ξ∈ Ω with radius ε>0. Precisely, given a small parameter ρ>0 and any integer m≥ 2, there exist a radius ε=ε(ρ)>0 small enough such that each sinh-Poisson type equation, either in Liouville form or mean field form, has a solution u_ρ with an asymptotic profile as a sign-changing tower of m singular Liouville bubbles centered at the same ξ and with ε(ρ)→ 0⁺ as ρ approaches to zero.

Related

• Sign-changing tower of bubbles for a sinh-Poisson equation with asymmetric exponents
• Bubbling solutions for mean field equations with variable intensities on compact Riemann surfaces
• Sign-changing bubble tower solutions for a Paneitz-type problem
• A note on a sinh-Poisson type equation with variable intensities on pierced domains
• Minimal blow-up masses and existence of solutions for an asymmetric sinh-Poisson equation