# Christina Lienstromberg

Frau Jun.-Prof. Dr.

Professorin - Leiterin der Abteilung für Differentialgleichungen

Institut für Analysis, Dynamik und Modellierung

Abteilung für Differentialgleichungen

## Kontakt

Pfaffenwaldring 57

70569 Stuttgart

Deutschland

Raum: 8.560

## Sprechstunde

Terminvereinbarung und Anfragen per E-Mail.

### Forschungsgebiet: Applied Analysis

- Partial differential equations and free-boundary value problems
- Modelling and analysis of non-Newtonian thin fluid films
- Rimming flows
- Data-driven fluid dynamics

- C. Lienstromberg und J. J. L. Velázquez, „Long-time asymptotics and regularity estimates for weak solutions to a doubly degenerate thin-film equation in the Taylor-Couette setting“. arXiv, to appear in Pure and Applied Analysis, 2023. doi: 10.48550/ARXIV.2203.00075.
- P. Gladbach, J. Jansen, und C. Lienstromberg, „Non-Newtonian thin-film equations: global existence of solutions, gradient-flow structure and guaranteed lift-off“, 2023, doi: 10.48550/ARXIV.2301.10300.
- C. Lienstromberg, S. Schiffer, und R. Schubert, „A variational approach to the non-newtonian Navier-Stokes equations“, 2023. doi: doi:10.48550/ARXIV.2312.03546.
- C. Lienstromberg, S. Schiffer, und R. Schubert, „A data-driven approach to viscous fluid mechanics: The stationary case“,
*Arch. Rational Mech. Anal.*, Bd. 247, Nr. 30, Art. Nr. 30, 2023, doi: 10.1007/s00205-023-01849-w. - O. Assenmacher, G. Bruell, und C. Lienstromberg, „Non-Newtonian two-phase thin-film problem: local existence, uniqueness, and stability“,
*Comm. Partial Differential Equations*, Bd. 47, Nr. 1, Art. Nr. 1, 2022, doi: 10.1080/03605302.2021.1957929. - J. Jansen, C. Lienstromberg, und K. Nik, „Long-time behaviour and stability for quasilinear doubly degenerate parabolic equations of higher order“. arXiv, 2022. doi: 10.48550/ARXIV.2204.08231.
- C. Lienstromberg, T. Pernas-Castano, und J. J. L. Velázquez, „Analysis of a two-fluid Taylor-Couette flow with one non-Newtonian fluid“,
*J. Nonlinear Sci.*, Bd. 32, Nr. 2, Art. Nr. 2, 2022, doi: 10.1007/s00332-021-09750-0. - J. Escher, P. Knopf, C. Lienstromberg, und B.-V. Matioc, „Stratified periodic water waves with singular density gradients“,
*Ann. Mat. Pura Appl. (4)*, Bd. 199, Nr. 5, Art. Nr. 5, 2020, doi: 10.1007/s10231-020-00950-1. - C. Lienstromberg und S. Müller, „Local strong solutions to a quasilinear degenerate fourth-order thin-film equation“,
*NoDEA Nonlinear Differential Equations Appl.*, Bd. 27, Nr. 2, Art. Nr. 2, 2020, doi: 10.1007/s00030-020-0619-x. - J. Escher und C. Lienstromberg, „Travelling waves in dilatant non-Newtonian thin films“,
*J. Differential Equations*, Bd. 264, Nr. 3, Art. Nr. 3, 2018, doi: 10.1016/j.jde.2017.10.015. - J. Escher, P. Gosselet, und C. Lienstromberg, „A note on model reduction for microelectromechanical systems“,
*Nonlinearity*, Bd. 30, Nr. 2, Art. Nr. 2, 2017, doi: 10.1088/1361-6544/aa4ff9. - C. Lienstromberg, „Well-posedness of a quasilinear evolution problem modelling MEMS with general permittivity“,
*J. Evol. Equ.*, Bd. 17, Nr. 4, Art. Nr. 4, 2017, doi: 10.1007/s00028-016-0375-x. - J. Escher und C. Lienstromberg, „A survey on second-order free boundary value problems modelling MEMS with general permittivity profile“,
*Discrete Contin. Dyn. Syst. Ser. S*, Bd. 10, Nr. 4, Art. Nr. 4, 2017, doi: 10.3934/dcdss.2017038. - J. Escher und C. Lienstromberg, „Finite-time singularities of solutions to microelectromechanical systems with general permittivity“,
*Ann. Mat. Pura Appl. (4)*, Bd. 195, Nr. 6, Art. Nr. 6, 2016, doi: 10.1007/s10231-016-0549-8. - J. Escher und C. Lienstromberg, „A qualitative analysis of solutions to microelectromechanical systems with curvature and nonlinear permittivity profile“,
*Comm. Partial Differential Equations*, Bd. 41, Nr. 1, Art. Nr. 1, 2016, doi: 10.1080/03605302.2015.1105259. - C. Lienstromberg, „On qualitative properties of solutions to microelectromechanical systems with general permittivity“,
*Monatsh. Math.*, Bd. 179, Nr. 4, Art. Nr. 4, 2016, doi: 10.1007/s00605-015-0744-5. - C. Lienstromberg, „A free boundary value problem modelling microelectromechanical systems with general permittivity“,
*Nonlinear Anal. Real World Appl.*, Bd. 25, S. 190--218, 2015, doi: 10.1016/j.nonrwa.2015.03.008.

##### Abteilung für Differentialgleichungen

**PromotionsstudierendeJuri Joussen M.Sc. **

**Espen Xylander M.Sc.**

**Masterstudierende**Adrian Schoch B.Sc.

SimTech Projekt PN 3-13 "A Data-Driven Approach to Viscous Fluid Dynamics"

im Exzellenzcluster EXC 2075 „Daten-integrierte Simulationswissenschaft“.

**Workshops**

**Analysis and Numerics on Nonlinear PDEs: Degenaries & Free Boundaries**03.-07.07.2023 - Lorentz Center Leiden

**International Conference on Data-Integrated Simulation Science (SimTech2023)**

04.-06.10.2023 - Universität Stuttgart

**Guests**

27.02.-03.03.2023 | Dr. Richard Schubert (Universität Bonn) |

26.02.-05.03.2023 | Dr. Stefan Schiffer (MPI Leipzig) |

27.01.-04.02.2023 | Dr. Jonas Jansen (Lund University) |

26.01.-04.02.2023 | Dr. Katerina Nik (Universität Wien) |

22.-29.01.2023 | Dr. Stefan Schiffer (MPI Leipzig) |

08.-14.01.2023 | Dr. Jonas Jansen (Lund University) |

08.-11.2023 | Dr. Gabriele Brüll (Lund University) |

01.-02.12.2022 | Dr. Richard Schubert (Universität Bonn) |

20.05.2022 | Dr. Richard Schubert (Universität Bonn) |

*Long-Time Behaviour of Solutions to Non-Newtonian Thin-Film Equations, *PDE-Seminar in Delft, 03.11.2022

*Long-Time Behaviour of Solutions to Non-Newtonian Thin-Film Equations, *Conference "Recent Trends in Fluid Mechanics" am ICMAT Madrid, 26.09.2022

*Long-Time Behaviour of Solutions to Non-Newtonian Thin-Film Equations, *

Arbeitsgruppenseminar der "AG Nichtlineare Partielle Differentialgleichungen" in Karlsruhe, 17.05.2022

Forschungsseminar "Seminar on PDE in the Sciences" in Bonn, 08.04.2022

**Lehre im Wintersemester 2023/2024**

- Vorlesung "Partielle Differenzialgleichungen und Modellierung"
- Stuttgart-Lund Joint Research Seminar "Asymptotics Models in Fluid Dynamics"
- Oberseminar Nichtlineare Differentialgleichungen

**Vorlesungen**

- SoSe 2023: Einführung in die Partiellen Differentialgleichung
- WiSe2022/23: Analytic semigroups and parabolic evolution equations
- SoSe 2022: Strongly continuous semigroups and hyperbolic evolution equations.

**Seminare**

- SoSe 2022: Thin-film flows with non-trivial dynamics (Masterseminar)

Masterarbeiten:

- A justification of the thin-film approximation for the Stokes flow (2023)
- Global Weak Solutions to the Ellis Thin-Film Equation (2022)
- A free-boundary problem for the Newtonian thin-film equation with mobilities hn, n ∈ (1, 2) and some aspects on the non-Newtonian case (2022)
- Non-Newtonian two-phase thin-film problems; Local Existence, uniqueness and stability (2021)
- Transport-Reaction Models (2021)

### Sekretariat:

### Elke Peter

Sekretariat am Lehrstuhl für Analysis und Mathematische Physik

[Foto: Robin Lang, 2018]