Titles & Abstracts
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Speaker: Yvan Martel (UVSQ - Université Paris-Saclay and Institut Universitaire de France)
Title: Non-existence of internal mode for the 1D Zakharov system
Abstract:
We prove that the linearized operator around any sufficiently small solitary wave of the one-dimensional Zakharov system has no internal mode. This spectral result is expected to play a role in any attempt to study the asymptotic stability of small solitary waves for this model.
Work in collaboration with Guillaume Rialland (UVSQ, France).
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Speaker: Michael McNulty (Universität zu Köln)
Title: Stable blowup for the higher-dimensional Skyrme model
Abstract:
The Skyrme model is a geometric field theory and a quasilinear modification of the nonlinear sigma model, i.e., wave maps into the sphere. In 3+1 dimensions, it is known that this modification prevents self-similar collapse and that global existence holds for large data. I will discuss recent work which demonstrates that this is not the case in 5+1 dimensions. In particular, Skyrme’s modification provides a stable mechanism for finite-time blowup at the self-similar rate.
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Speaker: Ruoyuan Liu (Universität Bonn)
Title: Global dynamics and weak universality for the fractional hyperbolic Φ^4_3-model
Abstract:
In this talk, I consider the 3-dimensional stochastic damped fractional
nonlinear wave equation (with order α > 1) with a cubic nonlinearity,
also known as the fractional hyperbolic Φ^4_3-model. The construction
of the fractional Φ^4_3-measure (Gibbs measure for the fractional
hyperbolic Φ^4_3-model) exhibits a phase transition: when α >
9/8, the Gibbs measure is equivalent with the base Gaussian measure; when
1 < α <= 9/8, the Gibbs measure is mutually singular with the base
Gaussian measure. I will first talk about global well-posedness of the
fractional hyperbolic Φ^4_3-model and invariance of the fractional
Φ^4_3-measure for the entire range α > 1. Then, I will discuss
weak universality for the fractional hyperbolic Φ^4_3-model. In the
case α > 9/8, we prove weak universality by using a first order
expansion, invariance of Gibbs measures, and space-time analysis. In the
case 1 < α <= 9/8, we also obtain weak universality by overcoming the
issue of singularity between the Gibbs measure and the base Gaussian
measure.
Some parts of the talk are based on a joint work with Nikolay Tzvetkov
(ENS Lyon) and Yuzhao Wang (University of Birmingham).
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