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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:

@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}
}

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