Regularities of the Navier-Stokes equations for incompressible or compressible viscous flows on bounded singular domains

- Title
- Regularities of the Navier-Stokes equations for incompressible or compressible viscous flows on bounded singular domains

- Authors
- 권오성

- Date Issued
- 2013

- Publisher
- 포항공과대학교

- Abstract
- In this dissertation we study incompressible or compressible viscous Navier-Stokes equations. For incompressible Navier-Stokes equations we use a plane
domain with non-convex corners and assign the non-standard boundary conditions on its boundaries. We construct the corner singularity functions for the Stokes operator with zero vorticity and velocity normal component
boundary conditions, subtract the corner singularities from the solution and show increased regularity for the remainder. For compressible viscous Navier-Stokes equations we use a finite non-convex polyhedral cylinder in R^3 and assign the Dirichlet boundary conditions on its boundaries. We split the edge singularity from the velocity solution and show the H^{2,q}xH^{1,q}-regularity
for the velocity remainder and the pressure where 3 < q < 1/(1-π/β) and β is the angle of the edge. The edge flux coefficient is well-defined in H^{2/q'-π/β,q}(-1,1) and the pressure singularity is propagated along the streamline and its derivatives blow up across the streamlines.

- URI
- http://postech.dcollection.net/jsp/common/DcLoOrgPer.jsp?sItemId=000001557054

http://oasis.postech.ac.kr/handle/2014.oak/1779

- Article Type
- Thesis

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