Publikation: The spin-coating process : analysis of the free boundary value problem
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2011
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Communications in Partial Differential Equations. 2011, 36(7), pp. 1145-1192. ISSN 0360-5302. Available under: doi: 10.1080/03605302.2010.546469
Zusammenfassung
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.
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510 Mathematik
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Free boundary, Navier slip, Navier-Stokes, Newton polygon, spin-coating, surface tension
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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. 2011, 36(7), pp. 1145-1192. ISSN 0360-5302. Available under: doi: 10.1080/03605302.2010.546469BibTex
@article{Denk2011spinc-19143,
year={2011},
doi={10.1080/03605302.2010.546469},
title={The spin-coating process : analysis of the free boundary value problem},
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}
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<dcterms:abstract xml:lang="eng">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.</dcterms:abstract>
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