### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 1145-1192 |

Number of pages | 48 |

Journal | Communications in Partial Differential Equations |

Volume | 36 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2011 Jul |

Externally published | Yes |

### Fingerprint

### Keywords

- Free boundary
- Navier slip
- Navier-Stokes
- Newton polygon
- Spincoating
- Surface tension

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Communications in Partial Differential Equations*,

*36*(7), 1145-1192. https://doi.org/10.1080/03605302.2010.546469

**The spin-coating process : Analysis of the free boundary value problem.** / Denk, Robert; Geissert, Matthias; Hieber, Matthias Georg; Saal, Jürgen; Sawada, Okihiro.

Research output: Contribution to journal › Article

*Communications in Partial Differential Equations*, vol. 36, no. 7, pp. 1145-1192. https://doi.org/10.1080/03605302.2010.546469

}

TY - JOUR

T1 - The spin-coating process

T2 - Analysis of the free boundary value problem

AU - Denk, Robert

AU - Geissert, Matthias

AU - Hieber, Matthias Georg

AU - Saal, Jürgen

AU - Sawada, Okihiro

PY - 2011/7

Y1 - 2011/7

N2 - 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.

AB - 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.

KW - Free boundary

KW - Navier slip

KW - Navier-Stokes

KW - Newton polygon

KW - Spincoating

KW - Surface tension

UR - http://www.scopus.com/inward/record.url?scp=79958167438&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79958167438&partnerID=8YFLogxK

U2 - 10.1080/03605302.2010.546469

DO - 10.1080/03605302.2010.546469

M3 - Article

AN - SCOPUS:79958167438

VL - 36

SP - 1145

EP - 1192

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

SN - 0360-5302

IS - 7

ER -