Lp estimates of solutions of some partial differential equations Original Research Article

The author is concerned with the long time asymptotic behaviors of the global weak solutions of some nonlinear evolution equations. First of all, he derives some uniform L1 and L∞ upper bounds for the solutions, under some mild conditions. Then, by applying the well-known Fourier splitting method and the L1 estimates, he asserts the L2 decay estimates of the solutions. The rates of decay are sharp in the sense that the integral of the initial data over View the MathML source is nonzero.