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초록
We present an explicit upper-bound for the life-span of C-3-smooth solutions to the multi-dimensional compressible Euler equations with a certain class of initial data containing compression vacuum states. We also show that the divergence of a fluid velocity will blow up along the particle trajectories issued from the compression vacuum states, which represent a shock formation at the vacuum states.
키워드
Compressible Euler equations; blow-up; shock wave; particle trajectory; vacuum boundary; PARTIAL-DIFFERENTIAL-EQUATIONS; NAVIER-STOKES EQUATIONS; SMOOTH SOLUTIONS; VACUUM STATES; BLOW-UP; SINGULARITIES; BEHAVIOR; WAVES
- 제목
- ON THE FORMATION OF SHOCKS TO THE COMPRESSIBLE EULER EQUATIONS
- 저자
- Chae, Dongho; Ha, Seung-Yeal
- 발행일
- 2009-09
- 유형
- Article
- 권
- 7
- 호
- 3
- 페이지
- 627 ~ 634