Zusammenfassung
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. ...
Zusammenfassung
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.
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