Fischer Group

Theory of Partial Differential Equations, Applied and Numerical Analysis

Diverse phenomena such as the motion of fluids or elastic objects, the evolution of interfaces, or the physics of quantum-mechanical particles are described accurately by partial differential equations. The Fischer group works on the mathematical analysis of partial differential equations that arise in the sciences, connecting also to areas like numerical analysis or probability.

Partial differential equations are a fundamental tool for the description of many phenomena in the sciences, ranging from the physics of continua like fluids or elastic solids over quantum mechanics to population biology. Julian Fischer and his group work on the mathematical aspects of partial differential equations. One of the group’s main themes is the mathematical justification of model simplifications: For example, an elastic material with a highly heterogeneous small-scale structure may in many cases be approximated as a homogeneous material. Likewise, a fluid with low compressibility may in many cases be approximated as ideally incompressible. To justify such approximations, the group derives rigorous estimates for the approximation error. The techniques they employ connect the analysis of PDEs with adjacent mathematical areas like numerical analysis and probability.


On this site:


Team


Current Projects

Effective behavior of random materials | Evolution of interfaces in fluid mechanics and solids | Structure of fluctuations in stochastic homogenization | Entropy-dissipative PDEs


Publications

Agresti A, Veraar M. 2022. Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence. Nonlinearity. 35(8), 4100–4210. View

Duerinckx M, Fischer JL, Gloria A. 2022. Scaling limit of the homogenization commutator for Gaussian coefficient  fields. Annals of applied probability. 32(2), 1179–1209. View

Fischer JL, Hopf K, Kniely M, Mielke A. 2022. Global existence analysis of energy-reaction-diffusion systems. SIAM Journal on Mathematical Analysis. 54(1), 220–267. View

Abbatiello A, Bulíček M, Maringová E. 2021. On the dynamic slip boundary condition for Navier-Stokes-like problems. Mathematical Models and Methods in Applied Sciences. 31(11), 2165–2212. View

Hensel S. 2021. Curvature driven interface evolution: Uniqueness properties of weak solution concepts. IST Austria. View

View All Publications

ReX-Link: Julian Fischer


Career

since 2017 Assistant Professor, Institute of Science and Technology Austria (ISTA)
2014 – 2016 Postdoc, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
2013 – 2014 Postdoc, University of Zurich, Switzerland
2013 PhD, University of Erlangen-Nürnberg, Germany


Selected Distinctions

2020 ERC Starting Grant
2020 ÖMG-Förderungspreis, Early-/Mid-Career-Award of the Austrian Mathematical Society
2015 Dr. Körper Prize, PhD Award of the GAMM


Additional Information

Open Julian Fischer’s website
Go to Mathematics at IST Austria website
Go to Mathphys Analysis Seminar website



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