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
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.
scientific article; zbMATH DE number 687519