Quasilinear Evolution Equations in [L.sup.P.sub.[mu]]-Spaces with Lower Regular Initial Data

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Quasilinear Evolution Equations in [L.sup.P.sub.[mu]]-Spaces with Lower Regular Initial Data

Zhang, Qinghua

Journal of function spaces, 01/2018, Volume: 2018

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We study the Cauchy problem of the quasilinear evolution equations in L.sup.P.sub.mu-spaces. Based on the theories of maximal L.sup.p-regularity of sectorial operators, interpolation spaces, and time-weighted L.sup.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 in L.sup.p,q-spaces with temporal weights.

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Zhang, Qinghua

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