Type of Publication:  Journal article 
Author:  Denk, Robert; Geissert, Matthias; Hieber, Matthias; Saal, Jürgen; Sawada, Okihiro 
Year of publication:  2011 
Published in:  Communications in Partial Differential Equations ; 36 (2011), 7.  pp. 11451192.  ISSN 03605302 
DOI (citable link):  https://dx.doi.org/10.1080/03605302.2010.546469 
Summary: 
In this paper, an accurate model of the spincoating process is presented and investigated from the analytical point of view. More precisely, the spincoating process is being described as a onephase free boundary value problem for Newtonian fluids subject to surface tension and rotational effects. It is proved that for T > 0 there exists a unique, strong solution to this problem in (0, T) belonging to a certain regularity class provided the data and the speed of rotation are small enough in suitable norms. The strategy of the proof is based on a transformation of the free boundary value problem to a quasilinear evolution equation on a fixed domain. The keypoint for solving the latter equation is the socalled maximal regularity approach. In order to pursue in this direction one needs to determine the precise regularity classes for the associated inhomogeneous linearized equations. This is being achieved by applying the Newton polygon method to the boundary symbol.

Subject (DDC):  510 Mathematics 
Keywords:  Free boundary, Navier slip, NavierStokes, Newton polygon, spincoating, surface tension 
Bibliography of Konstanz:  Yes 
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DENK, Robert, Matthias GEISSERT, Matthias HIEBER, Jürgen SAAL, Okihiro SAWADA, 2011. The spincoating process : analysis of the free boundary value problem. In: Communications in Partial Differential Equations. 36(7), pp. 11451192. ISSN 03605302. Available under: doi: 10.1080/03605302.2010.546469
@article{Denk2011spinc19143, title={The spincoating process : analysis of the free boundary value problem}, year={2011}, doi={10.1080/03605302.2010.546469}, number={7}, volume={36}, issn={03605302}, journal={Communications in Partial Differential Equations}, pages={11451192}, author={Denk, Robert and Geissert, Matthias and Hieber, Matthias and Saal, Jürgen and Sawada, Okihiro} }