The PhD defence will be in Abels utsikt - Niels Henrik Abels hus. The host of the session will moderate the technicalities while the chair of the defence will moderate the disputation.
Ex auditorio questions: the chair of the defence will invite the audience to ask questions ex auditorio at the end of the defence.
Trial lecture
Wednesday February 18th, time: 10:15 am, room 1259 (Abels utsikt).
Convex integration for the compressible Euler equations
Main research findings
Conservation laws are crucial mathematical models for predicting how quantities flow, describing phenomena ranging from rush-hour traffic to gas dynamics. These models face a fundamental mathematical challenge: They often predict the formation of "shocks"—sudden discontinuities, like a traffic jam. This, in turn, has the effect that the equations allow for multiple solutions, requiring a selection criterion to select the single, physically correct outcome.
This thesis establishes a new framework for identifying this correct, macroscopic solution, by shifting focus to the underlying microscopic dynamics. Instead of analyzing the solution as a whole, we track the specific trajectories along which mass and information travel. We prove that the stability of these trajectories is mathematically equivalent to selecting the physically correct solution.
We apply this insight to design a new, precise method for approximation and computer simulation of traffic flow. Furthermore, we demonstrate that introducing random noise to the equation acts as a natural selection mechanism: Rather than creating disorder, the noise regularizes the system, automatically forcing it to converge to the correct deterministic solution.
The work provides mathematicians and engineers with a unified framework to better understand and simulate scalar conservation laws.
Candidate contact information
LinkedIn: www.linkedin.com/in/magnusco
Adjudication committee
- Professor Christian Rohde, Universität Stuttgart
- Professor Gui-Qiang Chen, University of Oxford
- Professor Kenneth H. Karlsen, University of Oslo
Supervisors
- Professor Ulrik Skre Fjorholm, University of Oslo
- Professor Frank Norbert Proske, University of Oslo
Chair of defence
Head of Department Arne Bang Husby
Host of the session
Professor Kenneth H. Karlsen, University of Oslo