**中科院数学与系统科学研究院**

**数学研究所**

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**偏微分方程研讨班**

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Speaker：Prof.

Time：3:40-4:40pm, May 16, 2013

Place：Room 510, Morningside Center

Abstract: This talk concerns the well-posedness theory of the motion of physical vacuum for the compresssible Euler equations with or without self-grivatation. First, a general uniqueness theorem of classical solutions is proved for the three dimensional general motion. Second, for the spherically symmetric motions, without imposing the compatibility condition of the first derivative being zero at the center of symmetry, a new local-in-time existence theory is established in a new functional space involving less derivatives than those constructed for three-dimensional motion by constructing suitable weight and cutoff functions featuring the behavior of solutions near both the center of the symmetry and the moving vacuum boundary.

Place：Room 510, Morningside Center

Abstract: This talk concerns the well-posedness theory of the motion of physical vacuum for the compresssible Euler equations with or without self-grivatation. First, a general uniqueness theorem of classical solutions is proved for the three dimensional general motion. Second, for the spherically symmetric motions, without imposing the compatibility condition of the first derivative being zero at the center of symmetry, a new local-in-time existence theory is established in a new functional space involving less derivatives than those constructed for three-dimensional motion by constructing suitable weight and cutoff functions featuring the behavior of solutions near both the center of the symmetry and the moving vacuum boundary.