The existence and uniqueness of the generalized solution of the inverse problem for the nonlinear nonstationary Navier-Stokes system in the case of integral overdetermination
type: Item
instance of: scholarly article
title: The existence and uniqueness of the generalized solution of the inverse problem for the nonlinear nonstationary Navier-Stokes system in the case of integral overdetermination
zbMATH Open document ID: 0818.76013
DOI: 10.1007/BF01210419
author: I. A. Vasin
published in: Mathematical Notes
publication date: 1994-11-16T00:00:00Z
review text: The Navier-Stokes equations for incompressible fluid flow with inhomogeneous term in the form \(F(x,t) = f(t) g(x,t)\) and the integral overdetermination condition \[ \int_ \Omega V(x,t) \omega (x)dx = \varphi (t) \] are studied in the paper. The functions \(g, \omega, \varphi\) are given. The velocity field \(V(x,t)\) and the parameter \(f(t)\) have to be determined. The author proves the unique solvability of this inverse problem in a generalised form. The proof is based on the smart use of the contraction mapping theorem.
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35R30
zbMATH DE Number: 687519
zbMATH Keywords: contraction mapping theorem
reviewed by: P. B. Dubovski
MaRDI profile type: Publication
cites work: Q3031375
cites work: On a non-linear non-stationary inverse problem of hydrodynamics
cites work: Q3488464
description: scientific article; zbMATH DE number 687519