Research reports

Analytic regularity of solutions to the Navier-Stokes equations with mixed boundary conditions in polygons

by Y. He and C. Marcati and Ch. Schwab

(Report number 2021-29)

Abstract
We prove weighted analytic regularity of Leray-Hopf variational solutions for the stationary, incompressible Navier-Stokes Equations (NSE) in plane polygons , subject to analytic body forces. We admit mixed boundary conditions which may change type at each corner. The weighted analytic regularity results are established in scales of corner-weighted Kondrat'ev spaces of finite order. The proofs rely on a priori estimates for the corresponding linearized boundary value problem in sectors in corner-weighted Sobolev spaces and on an induction argument for the weighted norm estimates on the quadratic nonlinear term in the NSE, in a polar frame.

Keywords:

BibTeX
@Techreport{HMS21_971,
  author = {Y. He and C. Marcati and Ch. Schwab},
  title = {Analytic regularity of solutions to the Navier-Stokes equations with mixed boundary conditions in polygons},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2021-29},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2021/2021-29.pdf },
  year = {2021}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).

JavaScript has been disabled in your browser