Christina Lienstromberg

1. With P. Gladbach & J. Jansen: Non-Newtonian thin-film equations: global existence of solutions, gradient-flow structure and guaranteed lift-off, arXiv: 2301.10300, 2023.
2. With S. Schiffer & R. Schubert: A data-driven approach to viscous fluid mechanics -- the stationary case, to appear in Archive for Rational Mechanics and Analysis, arXiv:2207.00324, 2023.
3. With J. Jansen & K. Nik: Long-time behaviour and stability for quasilinear doubly degenerate parabolic equations of higher order; SIAM Journal on Mathematical Analysis, arXiv:2204.08231, 2023.
4. With 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:2203.00075, 2022.
5. With O. Assenmacher & G. Bruell: Non-Newtonian two-phase thin-film problem: Local existence, uniqueness, and stability; Comm. PDE 47, pp. 197--232, 2021.
6. With T. Pernas-Castaño & J. J. L. Velázquez: Analysis of a two-fluid Taylor-Couette flow with one non-Newtonian fluid; J. Nonlinear Sci. 32, 2021.
7. With J. Escher, P. Knopf & B.-V. Matioc: Stratified periodic water waves with singular density gradients. Ann. Mat. Pura Appl. 199, pp. 1923–1959, 2020.
8. With Stefan Müller: Local strong solutions to a quasilinear degenerate fourth-order thin-film equation. NoDEA. 27, 2020.
9. With J. Escher: Travelling waves in dilatant non-Newtonian thin films; J. Differential Equations 264, pp. 2113–2132, 2018.
10. With J. Escher: A survey on second-order free boundary value problems modelling MEMS with general permittivity. Discrete Contin. Dyn. Syst. Ser S10,  no. 4, pp. 745–771, 2017.
11. With J. Escher & P. Gosselet: A note on model reduction for microelectromechanical systems. Nonlinearity 30, pp. 454–465, 2017.
12. Well-posedness of a quasilinear evolution problem modelling MEMS with general permittivity. J. Evol. Equ. 17, pp. 1129–1150, 2017.
13. With J. Escher: Finite-time singularities of solutions to microelectromechanical systems with general permittivity. Ann. Mat. Pura Appl. 195, pp. 1961–1976, 2016.
14. On qualitative properties of solutions to microelectromechanical systems with general permittivity. Monatsh. Math. 179, pp. 581–602, 2016.
15. With J. Escher: A qualitative analysis of solutions to microelectromechanical systems with curvature and nonlinear permittivity profile. Comm. PDE 41, pp. 134–149, 2016.
16. A free boundary value problem modelling microelectromechanical systems with general permittivity. Nonlinear Anal. Real World Appl. 25, pp. 190–218, 2015

Research Group on Differntial Equations

PhD Students
Juri Joussen M.Sc.
Espen Xylander M.Sc.

Masterstudents
Adrian Schoch B.Sc.

Simulation Technology Project PN 3-13 "A Data-Driven Approach to Viscous Fluid Dynamics"

as part of the Cluster of Excellence EXC 2075 „Data-Integrated Simulation Science“.

• Stuttgart-Lund Joint Research Seminar "Asymptotics Models in Fluid Dynamics"
• Oberseminar Nichtlineare Differentialgleichungen

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

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" at ICMAT Madrid, 26.09.2022

Long-Time Behaviour of Solutions to Non-Newtonian Thin-Film Equations,
Group seminar der "AG Nichtlineare Partielle Differentialgleichungen" at Karlsruhe, 17.05.2022

Research seminar "Seminar on PDE in the Sciences" in Bonn, 08.04.2022

Winter Term 2023/2024

• Lecture "Partielle Differentialgleichung und Modellierung"
• Stuttgart-Lund Joint Research Seminar "Asymptotics Models in Fluid Dynamics"
• Oberseminar Nichtlineare Differentialgleichungen

Lectures

• Summer Term 2023: Einführung in die Partiellen Differentialgleichung
• Winter Term 2022/23: Analytic semigroups and parabolic evolution equations
• Summer Term 2022: Strongly continuous semigroups and hyperbolic evolution equations.

Seminars

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

Mastertheses:

• 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)