The spin-coating process : analysis of the free boundary value problem

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. 1145-1192. - ISSN 0360-5302
DOI (citable link): https://dx.doi.org/10.1080/03605302.2010.546469
Summary:
In this paper, an accurate model of the spin-coating process is presented and investigated from the analytical point of view. More precisely, the spin-coating process is being described as a one-phase 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 so-called 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, Navier-Stokes, Newton polygon, spin-coating, surface tension
Bibliography of Konstanz: Yes

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DENK, Robert, Matthias GEISSERT, Matthias HIEBER, Jürgen SAAL, Okihiro SAWADA, 2011. The spin-coating process : analysis of the free boundary value problem. In: Communications in Partial Differential Equations. 36(7), pp. 1145-1192. ISSN 0360-5302. Available under: doi: 10.1080/03605302.2010.546469

@article{Denk2011spinc-19143, title={The spin-coating process : analysis of the free boundary value problem}, year={2011}, doi={10.1080/03605302.2010.546469}, number={7}, volume={36}, issn={0360-5302}, journal={Communications in Partial Differential Equations}, pages={1145--1192}, author={Denk, Robert and Geissert, Matthias and Hieber, Matthias and Saal, Jürgen and Sawada, Okihiro} }

Sawada, Okihiro Geissert, Matthias Hieber, Matthias Geissert, Matthias The spin-coating process : analysis of the free boundary value problem Hieber, Matthias 2011 2012-05-02T09:20:41Z Denk, Robert Denk, Robert Sawada, Okihiro Saal, Jürgen 2012-05-02T09:20:41Z Saal, Jürgen In this paper, an accurate model of the spin-coating process is presented and investigated from the analytical point of view. More precisely, the spin-coating process is being described as a one-phase 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 so-called 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. Publ. in: Communications in Partial Differential Equations ; 36 (2011), 7. - pp. 1145-1192 eng terms-of-use

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