Basic properties of solution of the non-steady Navier–Stokes equations with mixed boundary conditions in a bounded domain

Abstract

In this paper we deal with the system of the non-steady Navier-Stokes equations with mixed boundary conditions. We study the existence and uniqueness of a solution of this system. Suppose that the system is solvable with some given data (the initial velocity and the right hand side). We prove that there exists a unique solution of this system for data which are small perturbations of the previous ones.

Some properties on the surfaces of vector fields and its application to the Stokes and Navier–Stokes problems with mixed boundary conditions

“…[20][21][22]52,53] and references therein) or νε(v)n − pn = 0 (cf. [54,53] and references therein) also is used. Rotation boundary condition has been fairly extensively studied over the past several years.…”

“…[9,21,54,56,67]). When one deals with the mixed boundary conditions of velocity and the component of strain ε(u)n, for variational formulation of the problem the bilinear form…”

Robust Stabilization of Laminar Flows in Varying Flow Regimes

“…also the appendix in Nguyen and Raymond (2015). For small α or in the neighborhood of a known solution, existence can be stated using the arguments in Kučera (1998). In Hou and Ravindran (1998), existence has been proven for the case that there are no more pure Dirichlet boundary conditions.…”

Solutions to the Navier–Stokes equations with mixed boundary conditions in two‐dimensional bounded domains

“…Since (ϑ, q) solves equations (A.1)-(A.2), (w, Q) satisfies equations (A. 19) and (A.20) in K. LetS = {(ξ, ω) : ξ ∈ R, 0 < ω < π/2} be an infinite strip (see Fig. 4).…”