Critical spaces for quasilinear parabolic evolution equations and applications

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

Pruess, Jan¹  Simonett, Gieri²  Wilke, Mathias³ 

[1] Martin Luther Univ Halle Wittenberg, Inst Math, Theodor Lieser Str 5, D-06120 Halle, Germany

[2] Vanderbilt Univ, Dept Math, Nashville, TN 37235 USA

[3] Univ Regensburg, Fak Math, D-93040 Regensburg, Germany

关键词: Semilinear parabolic equations;    Quasilinear parabolic equations;    Critical spaces;    Navier-Stokes equations;    Vorticity equations;    Scaling invariance;   

DOI  :  10.1016/j.jde.2017.10.010

来源: Elsevier

【 摘 要 】

We present a comprehensive theory of critical spaces for the broad class of quasilinear parabolic evolution equations. The approach is based on maximal L-p-regularity in time-weighted function spaces. It is shown that our notion of critical spaces coincides with the concept of scaling invariant spaces in case that the underlying partial differential equation enjoys a scaling invariance. Applications to the vorticity equations for the Navier-Stokes problem, convection-diffusion equations, the Nernst-Planck-Poisson equations in electro-chemistry, chemotaxis equations, the MHD equations, and some other well-known parabolic equations are given. (c) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free