TBA by Levon Nurbekyan
- Series
- PDE Seminar
- Time
- Tuesday, April 22, 2025 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Levon Nurbekyan – Emory University – levon.nurbekyan@emory.edu
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Please Note: Please note the unusual time and place.
We prove that negative energy solutions to the modified Benjamin-Ono (mBO) equation, which is L^2 critical, with mass slightly above the ground state mass, blow-up in finite or infinite time. These blow-up solutions lie adjacent to those constructed by Martel & Pilod (2017) that have mass exactly equal to the ground state mass. The solutions that we construct, with mass slightly above the ground state mass, are numerically observable and expected to be stable. This is joint work with Svetlana Roudenko and Kai Yang.
The hydrostatic Euler equations, also known as the inviscid primitive equations, are derived from the Euler equations by taking the hydrostatic limit. They are commonly used when the aspect ratio of the domain is small, such as the ocean and atmosphere in the planetary scale. In this talk, I will first present the stability of finite-time blowup of smooth solutions to this model, then discuss the effect of fast rotation (from Coriolis force) in prolonging the lifespan of solutions. Finally, I will talk about the regularization effects that arise when the model is driven by certain random noise.
We will talk about recent work establishing a quantitative nonlinear scattering theory for asymptotically de Sitter solutions of the Einstein vacuum equations in (n+1) dimensions with n ≥ 4 even, which are determined by small scattering data at future infinity and past infinity. We will also explain why the case of even spatial dimension n poses significant challenges compared to its odd counterpart and was left open by the previous works in the literature.