This is the website of our weekly Hyperbolic & Dispersive PDE Seminar at Rutgers University. Welcome!
Organizers: Maxime Van de Moortel, Avy Soffer.
The topics covered by the seminar are very broad and also include, among others: General Relativity, Fluid Mechanics, Harmonic Analysis, Quantum Mechanics, Spectral Theory and Applied Mathematics, always with a strong emphasis on Analysis.
Speaker: Wilhelm Schlag Yale University
Title: On the long-term dynamics of nonlinear wave equations on the line with a critical potential
Abstract: We will present recent results with J. Krieger and K. Widmayer on a cubic NLS on the line with a repulsive inverse square potential. Some of the context in the wider space-time resonance and wave packet methods will be provided.
Speaker: David Ambrose Drexel University
Title: Some non-decaying, non-periodic existence theory for fluid equations
Abstract: We consider the irrotational Euler equations and the surface quasi-geostrophic equation in the case that the unknowns do not decay and are not spatially periodic. In such settings, constitutive laws of convolution type (such as the Biot-Savart law) do not apply directly, as the convolution integral does not converge. These can be replaced with identities of Serfati type, which separate the integrals into near-field and far-field pieces, with the far field contribution being able to be manipulated for better convergence properties. We use these identities to find existence of solutions for the 2D Euler equations with bounded velocity and vorticity (generalizing a result of Serfati), for the 3D Euler equations in uniformly local Sobolev spaces, and for SQG in Holder spaces and in uniformly local Sobolev spaces. This includes joint work with Elaine Cozzi, Daniel Erickson, James Kelliher, Milton Lopes Filho, and Helena Nussenzveig Lopes.
Speaker: Minh-Binh Tran Texas A&M University
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Speaker: Serban Cicortas Princeton University
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Speaker: Hamed Masaood Princeton University
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Speaker: Sanchit Chaturvedi NYU
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Speaker: Christoph Kehle MIT
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