Justin Valletta

activity

20232026

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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 $A = (- Δ)^{k}$ . We prove that for arbitrary radial initial data and a sign…

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…

Breakdown of smooth solutions to the subcritical EPDiff equation

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

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