Blowup for regular solutions and C¹ solutions of Euler equations in Rᴺ with a free boundary

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Abstract

The compressible Euler equations are fundamental models in the study of fluids, plasmas, condensed matter and atmospheric dynamics. In this paper, we analyze the blowup phenomena of the weakened regular solutions (ρ,u→) and the C¹ solutions for γ≥2 of the Euler equations in Rᶰ in an initial bounded region Ω(0). If maxx→₀∈∂Ω̄(0)∑Ni=1uᵢ ²(0,x→₀)<[Formula presented],where E is the total energy and M>0 is the total mass, then the corresponding solutions blow up in finite time. Our blowup development for the free boundary value problem partially complements the result for the fixed boundary problem (Makino et al. 1986). Copyright © 2017 Elsevier Masson SAS.
Original languageEnglish
Pages (from-to)427-432
JournalEuropean Journal of Mechanics, B/Fluids
Volume67
Early online dateOct 2017
DOIs
Publication statusPublished - 2018

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Regular Solution
free boundaries
Free Boundary
Euler Equations
Blow-up
Free Boundary Value Problems
Compressible Euler Equations
Blow-up Solution
Boundary Problem
boundary value problems
complement
Plasma
Complement
Fluid
fluids
Model

Bibliographical note

Yuen, M. (2018). Blowup for regular solutions and C¹ solutions of Euler equations in Rᴺ with a free boundary. European Journal of Mechanics - B/Fluids, 67, 427-432.

Keywords

  • Blowup
  • Classical solutions
  • Compressible Euler equations
  • Free boundary problems
  • Initial value problems
  • Regular solutions
  • Vacuum