%0 Journal Article
%T Existence and Uniqueness of Solutions to Nonlinear Evolution Equations with Locally Monotone Operators
%A Wei Liu
%J Mathematics
%D 2010
%I arXiv
%R 10.1016/j.na.2011.08.018
%X In this paper we establish the existence and uniqueness of solutions for nonlinear evolution equations on Banach space with locally monotone operators, which is a generalization of the classical result by J.L. Lions for monotone operators. In particular, we show that local monotonicity implies the pseudo-monotonicity. The main result is applied to various types of PDE such as reaction-diffusion equations, generalized Burgers equation, Navier-Stokes equation, 3D Leray-$\alpha$ model and $p$-Laplace equation with non-monotone perturbations.
%U http://arxiv.org/abs/1011.0562v1