On a local energy decay estimate of solutions to the hyperbolic type Stokes equations
The authors consider the initial-boundary value problem for the hyperbolic type Stokes equations of incompressible fluid flow in an exterior domain and in a perturbed half-space. The equations are a linearized version of the hyperbolic Navier-Stokes equations introduced by \textit{R. Racke} and \textit{J. Saal} [Evol. Equ. Control Theory 1, No. 1, 195--215 (2012; Zbl 1262.35171)], which are obtained from a Cattaneo-type law as a delayed case for the deformation tensor in the incompressible Navier-Stokes equations. A local energy decay estimate of solutions is derived using the approach of \textit{W. Dan} and \textit{Y. Shibata} [Funkc. Ekvacioj, Ser. Int. 38, No. 3, 545--568 (1995; Zbl 0848.35070)] for the dissipative wave equation.
scientific article; zbMATH DE number 6848974
scientific article