Pruess, Jan and Simonett, Gieri and Wilke, Mathias (2018) Critical spaces for quasilinear parabolic evolution equations and applications. JOURNAL OF DIFFERENTIAL EQUATIONS, 264 (3). pp. 2028-2074. ISSN 0022-0396, 1090-2732
Full text not available from this repository. (Request a copy)Abstract
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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CONVERGENCE; ENERGY; Semilinear parabolic equations; Quasilinear parabolic equations; Critical spaces; Navier-Stokes equations; Vorticity equations; Scaling invariance |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 20 Mar 2020 11:01 |
| Last Modified: | 20 Mar 2020 11:01 |
| URI: | https://pred.uni-regensburg.de/id/eprint/15059 |
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