On the Analyticity of Particle Trajectories in the Ideal Incompressible Fluid
作者: A. Shnirelman
刊名: Global and Stochastic Analysis, 2015, Vol.2 (2)
来源数据库: Mind Reader Publications
关键词: Ideal °uidEuler equationsgroup of di®eomorphismsanalyticityholomorphy in Banach spaces.
原始语种摘要: A new proof is given of the fact that the particle trajec- tories of the ideal incompressible °uid are analytic curves, though the solutions of the Euler equations may have a ¯nite regularity. This is a consequence of a general fact that the geodesic exponential map on the group of volume preserving di®eomorphisms belonging to the Sobolev space is real-analytic. The proof is based on the general properties of holomorphic maps in complex Banach spaces.
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  • geodesic 测地的
  • preserving 保藏
  • exponential 指数的
  • regularity 规则性
  • proof 证明
  • ideal 理想
  • complex 超群
  • incompressible 不可压缩的
  • analytic 解析的
  • general 普遍的