2012/08/28 by Daomin Cao, Zhongyuan Liu, Cao, Daomin +3
Engineering · Mathematics · Physics and Astronomy · #35J40(Secondary) #35J60(Primary) #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #math-ph #math.AP #math.MP
paper · pdf · doi:10.48550/arxiv.1208.5540
This paper is the continuation of the paper (arXiv:1208.3002v2), 35 pages
openalex publication_date 2012/08/28 · arxiv created 2012/10/30 · arxiv updated 2012/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we continue to construct stationary classical solutions of the incompressible Euler equation approximating singular stationary solutions of this equation. This procedure now is carried out by constructing solutions to the following elliptic problem cases -\ep2 Δu=(u-q-\fracκ2πln(1)/(\ep))+p-(q-\fracκ2πln(1)/(\ep)-u)+p, x∈Ω, u=0, x∈∂Ω, cases where p>1, Ω⊂ℝ2 is a bounded domain, q is a harmonic function. We showed that if Ω is a simply-connected smooth domain, then for any given non-degenerate critical point of Kirchhoff-Routh function W(x1+,...,xm+,x1-,...,xn-) with κ+i=κ>0 (i=1,...,m) and κ-j=-κ (j=1,...,n), there is a stationary classical solution approximating stationary m+n points vortex solution of incompressible Euler equations with total vorticity (m-n)κ.