On the fundamental solutions to stokes equations

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Abstract

We study the behavior of solutions to the stationary Stokes equations near singular points. Employing the power series expansions of harmonic and biharmonic functions, we have local power series expansions of solutions near singular points. Then we find the precise structures of homogeneous solutions near singular points which appear in local power series expansions. From the structures of the homogeneous solutions we characterize the fundamental solutions. Moreover, we study the asymptotic behavior of solutions to Stokes and Navier-Stokes equations under an assumption on directions of velocities.

Original languageEnglish
Pages (from-to)313-337
Number of pages25
JournalJournal of Differential Equations
Volume153
Issue number2
DOIs
Publication statusPublished - 1999 Apr 10

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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