
Mathematics 2011
Existence of weak solutions for the generalized NavierStokes equations with dampingAbstract: In this work we consider the generalized NavierStoke equations with the presence of a damping term in the momentum equation. % The problem studied here derives from the set of equations which govern the isothermal flow of incompressible, homogeneous and nonNewtonian fluids. % For the generalized NavierStokes problem with damping, we prove the existence of weak solutions by using regularization techniques, the theory of monotone operators and compactness arguments together with the local decomposition of the pressure and the Lipschitztruncation method. The existence result proved here holds for any $q>\frac{2N}{N+2}$ and any $\sigma>1$, where $q$ is the exponent of the diffusion term and $\sigma$ is the exponent which characterizes the damping term.
