Quasilinear Evolution Equations in LμP-Spaces with Lower Regular Initial Data. (2nd May 2018)

• Record Type: Journal Article
• Authors: Zhang, Qinghua
• Other Names: Ragusa Maria Alessandra Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2018(2018)
• Publication Date: 2018-05-02
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2018/2569080
• Languages: English
• ISSNs: 2314-8896

Abstract

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.