2019/02/28 by Daniel Ginsberg, Hans Lindblad, Chenyun Luo · 19 citations
Engineering · Mathematics · #Boundary (topology) #Boundary value problem #Classical mechanics #Compressibility #Compressible flow #Computational Fluid Dynamics and Aerodynamics #Dirichlet boundary condition #Equations of motion #Euler equations #Euler's formula #Free boundary problem #Free surface #Geometric Analysis and Curvature Flows #Geometry #Lagrangian #Lagrangian and Eulerian specification of the flow field #Mathematical analysis #Mathematics #Mechanics #Motion (physics) #Navier-Stokes equation solutions #Newtonian fluid #Physics #Smoothing #Surface (topology) #math.AP
paper · pdf · doi:10.1007/s00205-019-01477-3
published in Archive for Rational Mechanics and Analysis 236(2), 603-733 (Springer Science+Business Media) · Corrected typos
arxiv created 2019/05/17 · openalex publication_date 2019/11/30 · openalex created_date 2019/12/05 · arxiv updated 2020/01/08 · openalex updated_date 2026/08/05
We establish the local well-posedness for the free boundary problem for the compressible Euler equations describing the motion of liquid under the influence of Newtonian self-gravity. We do this by solving a tangentially-smoothed version of Euler's equations in Lagrangian coordinates which satisfies uniform energy estimates as the smoothing parameter goes to zero. The main technical tools are delicate energy estimates and optimal elliptic estimates in terms of boundary regularity, for the Dirichlet problem and Green's function.