Abstract
The existence, uniqueness and uniformly Lp 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 Lp estimates of solutions for numerous classes of Navier–Stokes type problems are obtained. In application, the existence, uniqueness and uniformly Lp 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.
Highlights
We consider the mixed problem for Navier–Stokes (N–S)-type equation with small parameter
The focus of our work was to prove uniform existence and uniqueness of the stronger local and global solution of the Navier–Stokes problem with a small parameter (1a)–(1c). This problem is characterized by the presence of an abstract operator A and a small parameter ε k that, respectively, corresponds to the inverse of a Reynolds number Re that is very large for the N–S equations
Banach spaces instead of E and concrete positive differential, pseudo differential operators, or finite, infinite matrices, etc. instead of A, by virtue of Theorem 3 and 4 we can obtain the maximal regularity properties of different class of stationary and instationary Stokes problems, respectively, which occur in numerous physics and engineering problems
Summary
Dipartimento di Matematica e Informatica, Universitá degli Studi di Catania, 95125 Catania, Italy. Azerbaijan State Economic University, Linking of Research Centers, Murtuz Mukhtarov, AZ1001 Baku, Azerbaijan. Received: 18 November 2020; Accepted: 16 December 2020; Published: 21 December 2020
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
