Justin Valletta

collaborators

3 papers

math.AP2025

Breakdown of smooth solutions to the subcritical EPDiff equation

Martin Bauer, Stephen C. Preston, Justin Valletta

We consider the EPDiff equation on $R^{n}$ with the integer-order homogeneous Sobolev inertia operator $A = (- I^)^{k}$ . We prove that for arbitrary radial initial data and a sig…

math.AP2025

Local well-posedness of the higher-dimensional $b$ -equation

Justin Valletta

The higher-dimensional $b$ -equation is a family of PDEs, introduced by Holm and Staley (2003), that describe the motion of shallow water waves in $n$ -dimensions. It expresses the i…

math.AP2024

Liouville comparison theory for blowup of Euler-Arnold equations

Martin Bauer, Stephen C. Preston, Justin Valletta

In this article we introduce a new blowup criterion for (generalized) Euler-Arnold equations on $R^{n}$ . Our method is based on treating the equation in Lagrangian coordinate…

Breakdown of smooth solutions to the subcritical EPDiff equation

Local well-posedness of the higher-dimensional b-equation

Liouville comparison theory for blowup of Euler-Arnold equations

Local well-posedness of the higher-dimensional $b$ -equation