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arXiv:1109.5217

已有 2677 次阅读 2011-9-27 22:39 |个人分类:数学文献|系统分类:科研笔记

Existence of weak solutions for the generalized Navier-Stokes equations with damping
 In this work we consider the generalized Navier-Stoke 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 non-Newtonian fluids. % For the generalized Navier-Stokes 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 Lipschitz-truncation 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.


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