A Navier-Stokes-Type Problem with High-Order Elliptic Operator and Applications

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Ragusa M. A., Shakhmurov V. B.

MATHEMATICS, vol.8, no.12, pp.1-23, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 12
  • Publication Date: 2020
  • Doi Number: 10.3390/math8122256
  • Journal Name: MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Page Numbers: pp.1-23
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

The existence, uniqueness and uniformly L-p estimates for solutions of a high-order abstract Navier-Stokes problem on half space are derived. The equation involves an abstract operator in a Banach space E and small parameters. Since the Banach space E is arbitrary and A is a possible linear operator, by choosing spaces E and operators A, the existence, uniqueness and L-p estimates of solutions for numerous classes of Navier-Stokes type problems are obtained. In application, the existence, uniqueness and uniformly L-p estimates for the solution of the Wentzell-Robin-type mixed problem for the Navier-Stokes equation and mixed problem for degenerate Navier-Stokes equations are established.