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

Author

Listed:
  • Maria Alessandra Ragusa

    (Dipartimento di Matematica e Informatica, Universitá degli Studi di Catania, 95125 Catania, Italy
    RUDN University, 6 Miklukho-Maklay St, Moscow 117198, Russia)

  • Veli B. Shakhmurov

    (Antalya Bilim University, Çiplakli Mah. Farabi Cad. 23 Dosemealti, 07190 Antalya, Turkey
    Azerbaijan State Economic University, Linking of Research Centers, Murtuz Mukhtarov, AZ1001 Baku, Azerbaijan)

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.

Suggested Citation

  • Maria Alessandra Ragusa & Veli B. Shakhmurov, 2020. "A Navier–Stokes-Type Problem with High-Order Elliptic Operator and Applications," Mathematics, MDPI, vol. 8(12), pages 1-23, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2256-:d:465723
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