On compactness, domain dependence and existence of steady state solutions to compressible isothermal Navier-Stokes equations

Pavel I. Plotnikov (1) , Jan Sokolowski (2)

1 Lavryentyev Institute of Hydrodynamics
2 IECN - Institut Élie Cartan de Nancy

The steady state system of isothermal Navier-Stokes equations is considered in two dimensional domain including an obstacle. The shape optimisation problem of minimisation of the drag with respect to the admissible shape of the obstacle is defined. The generalized solutions for the Navier-Stokes equations are introduced. The existence of an optimal shape is proved in the class of admissible domains. In general the solutions are not unique for the problem under considerations.

Mots clés: Compressible fluids; Navier-Stokes equations; Generalized solutions; Shape optimization; Drag minimization

Domaines: Equations aux dérivées partielles [math.AP]

Pavel I. Plotnikov, Jan Sokolowski. On compactness, domain dependence and existence of steady state solutions to compressible isothermal Navier-Stokes equations. Journal of Mathematical Fluid Mechanics, 2005, vol. 7 fasc. 4, pp.529-573. ⟨hal-00101957⟩