Algebraic L 2 Decay for Weak Solutions of the Nonlinear Heat Equations in Whole Space R 3

Abstract

We obtained the algebraic $L^2$ time decay rate for weak solutions of the nonlinear heat equations with the nonlinear term ${\left|\nabla u\right|}^{2}u$ in whole space ${\mathbf{R}}^3$. The methods are based on energy methods and Fourier analysis technique.