Regularity of Stagnation Point-form Solutions of the Two-dimensional\n Euler Equations

2013/06/20 by Alejandro Sarria, Sarria, Alejandro · 1 citation
Engineering · Mathematics · #35B10 #35B44 #35B65 #35Q35 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1306.4756

openalex publication_date 2013/06/20 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

A class of semi-bounded solutions of the two-dimensional incompressible Euler\nequations satisfying either periodic or Dirichlet boundary conditions is\nexamined. For smooth initial data, new blowup criteria in terms of the initial\nconcavity profile is presented and the effects that the boundary conditions\nhave on the global regularity of solutions is discussed. In particular, by\nderiving a formula for a general solution along Lagrangian trajectories, we\ndescribe how periodicity can prevent blow-up. This is as opposed to Dirichlet\nboundary conditions which, as we will show, allow for the formation of\nsingularities in finite time. Lastly, regularity of solutions arising from\nnon-smooth initial data is briefly discussed.\n

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