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Friday May 16, 2025

Phd Defense
Breakdown of higher-order Euler-Arnold equations
- Justin Valletta, FSU
Time: 2:30 Room: 216 Dirac
Abstract/Desc: The higher-dimensional $b$-equation is a family of PDEs describing the motion of shallow water waves in $n$-dimensions. When $b=2$, this family becomes the EPDiff equation, which has additional structure and obeys a variational principle. These families of PDEs have geometric interpretations as Euler-Arnold equations, i.e., as geodesic equations on certain diffeomorphism groups that allow them to be formulated as ODEs on appropriate Banach spaces. We exploit this fact to obtain results on local well-posedness for the $b$-equation and $C^1$ blow-up of solutions to EPDiff.

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Department of Mathematics

This Week in Mathematics