On the fundamental solutions to stokes equations

Hi Jun Choe

doi:10.1006/jdeq.1998.3558

On the fundamental solutions to stokes equations

Hi Jun Choe

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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 language	English
Pages (from-to)	313-337
Number of pages	25
Journal	Journal of Differential Equations
Volume	153
Issue number	2
DOIs	https://doi.org/10.1006/jdeq.1998.3558
Publication status	Published - 1999 Apr 10

Bibliographical note

Funding Information:
The author appreciates the valuable suggestions from the referee. He acknowledges the financial support of the Korea Research Foundation and KOSEF made in the program year of 1999.

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1006/jdeq.1998.3558

Cite this

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N2 - 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.

AB - 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.

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ER -

On the fundamental solutions to stokes equations

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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