Quasilinear Evolution Equations in LμP-Spaces with Lower Regular Initial Data. (2nd May 2018) - Zhang, Qinghua
Abstract : We study the Cauchy problem of the quasilinear evolution equations inL μ p -spaces. Based on the theories of maximalL p -regularity of sectorial operators, interpolation spaces, and time-weightedL p -spaces, we establish the local posedness for a class of abstract quasilinear evolution equations with lower regular initial data. To illustrate our results, we also deal with the second-order parabolic equations and the Navier-Stokes equations inL p, q -spaces with temporal weights.