Lecture Course : Fluid Mechanics, covering Rotational Water Waves and Rayleigh-Taylor Instabilities for Potential Flows

Start: Wednesday, March 4, 2026, 10:00 - 11:30 
Further dates:
Wednesday, March 4, 2026, 10:00 - 11:30 h
Tuesday, March 10, 2026, 10:00 - 11:30 h
Wednesday, March 11, 2026, 10:00 - 11:30 h
Thursday, March 19, 2026, 09:00 - 10:30 h
Tuesday, June 2, 2026, 09:00 - 10:30 h
End: Thursday, June 11, 2026, 10:00 - 11:30 h

Abstract: 
Fluid Mechanics is a key area in which progress at any time can be seen as a benchmark for evaluating the actual achievements of mathematical science. The course offers an introduction to modern aspects of Mathematical Fluid Mechanics. Some tools and methods from Analysis and Functional Analysis for dealing with nonlinear partial differential equations stemming from Fluid Mechanics will be presented. Starting from fundamental physical principles, the complete Euler system of hydrodynamics including free boundaries is derived. Building on this, two distinguished classes of hydrodynamic flows will be studied in detail: traveling waves and potential flows. Questions like existence, uniqueness, stability, regularity of solutions, or bifurcation and wave-breaking phenomena will be addressed.

Contents of the course:
• First principles and Euler’s equations
• Travelling waves for rotational 2D Euler flows
• Hodograph transformation
• Existence of large rotational waves
• Analyticity of rotational waves
• Dary’s law and potential flows
• Rayleigh-Taylor instabilities
• Bifurcation of fingering solutions

Requirements
The course in intended to contribute to the master programme of the Faculty of Mathematics at University of Vienna.
Requirements: Good knowledge in Analysis and Functional Analysis

Lecture Course Announcement (pdf)

Link to the course directory