Research

Research focus

The Mathematical Modeling group is led by Dominic Breit and focuses on nonlinear (stochastic) partial differential equations. An overview of previous research results can be found here. The application focus is on problems in fluid mechanics:

• Compressible fluids
• Stochastic Navier-Stokes equations
• Fluid-structure interaction
• Non-Newtonian fluids

On the theoretical side we are interested in:

• Regularity theory
• calculus of variations
• Function spaces

Finally, we do numerical analysis for problems related to the above topics.

An overview of previous research results can be found here.

All Publications

Click here to see all publications.

Selected Publications

D. Breit & A. Prohl: Error analysis for 2D stochastic Navier-Stokes equations in bounded domains with Dirichlet data. Found. Comp. Math. DOI:10.1007/s10208-023-09621-y

D. Breit: Regularity results in 2D fluid-structure interaction. Math. Ann. 388, 1495–1538. (2024)

D. Breit & S. Schwarzacher: Navier-Stokes-Fourier fluids interacting with elastic shells. Ann. Sc. Norm. Super. Pisa(5) XXIV, 619-690. (2023).

D. Breit, A. Cianchi, L. Diening & S. Schwarzacher: Global Schauder estimates for the p-Laplace system.Arch. Rational Mech. Anal. 243, 201-255. (2022).

D. Breit & A. Cianchi: Symmetric gradient Sobolev spaces endowed with rearrangement invariant norms.Adv. Math. 391, 107954. (2021).

D. Breit, L. Diening & F. Gmeineder: On the trace operator for functions of bounded A-variation. Anal. PDE 13, 559-594. (2020).

D. Breit, E. Feireisl & M. Hofmanova: Solution semiflow for the isentropic Euler system. arch. Rational Mech. Anal. 235, 167-194. (2020).

D. Breit, E. Feireisl, M. Hofmanova & B. Maslowski: Stationary solutions to the compressible Navier-Stokes system driven by stochastic forces.Probab. Theory Relat. Fields 174, 981-1032. (2019).

D. Breit, A. Cianchi, L. Diening, T. Kuusi & S. Schwarzacher: Pointwise Calderon- Zygmund gradient estimates for the p-Laplace system. J. Math. Pures Appl. 114, 146-190. (2018).

D. Breit & S. Schwarzacher: Compressible fluids interacting with a linear-elastic shell. Arch. Rational Mech. Anal. 228, 495-562. (2018)

D. Breit & M. Hofmanova: Stochastic Navier-Stokes equations for compressible fluids.Indiana Univ. Math. J. 65, 1183-1250. (2016).

D. Breit, L. Diening & S. Schwarzacher: Solenoidal Lipschitz truncation for parabolic PDEs. Math. mod. Meth. Appl. Sci. 23, 2671-2700. (2013).