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 language | English |
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Pages (from-to) | 427-432 |
Journal | European Journal of Mechanics, B/Fluids |
Volume | 67 |
Early online date | Oct 2017 |
DOIs | |
Publication status | Published - 2018 |
Citation
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