Quasilinear Evolution Equations in LμP-Spaces with Lower Regular Initial Data

Abstract EN

We study the Cauchy problem of the quasilinear evolution equations in Lμp-spaces.

Based on the theories of maximal Lp-regularity of sectorial operators, interpolation spaces, and time-weighted Lp-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 in Lp,q-spaces with temporal weights.