09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
›9:30 (1h)
Cyril Imbert
We will see that the Fisher information is monotone decreasing in time along solutions of the space-homogeneous Boltzmann equation for a large class of collision kernels covering all classical interactions derived from systems of particles. For general collision kernels, a sufficient condition for the monotonicity of the Fisher information along the flow is related to the best constant for an integro-differential inequality for functions on the sphere, which belongs in the family of the Log-Sobolev inequalities. As a consequence, we establish the existence of global smooth solutions to the space-homogeneous Boltzmann equation in the main situation of interest where this was not known, namely the regime of very soft potentials. Joint work with Luis Silvestre and Cédric Villani.
Fisher information for the Boltzmann equation.
We will see that the Fisher information is monotone decreasing in time along solutions of the space-homogeneous Boltzmann equation for a large class of collision kernels covering all classical interactions derived from systems of particles. For general collision kernels, a sufficient condition for the monotonicity of the Fisher information along the flow is related to the best constant for an integro-differential inequality for functions on the sphere, which belongs in the family of the Log-Sobolev inequalities. As a consequence, we establish the existence of global smooth solutions to the space-homogeneous Boltzmann equation in the main situation of interest where this was not known, namely the regime of very soft potentials. Joint work with Luis Silvestre and Cédric Villani.
9:30 - 10:30 (1h)
Cyril Imbert
Fisher information for the Boltzmann equation.
We will see that the Fisher information is monotone decreasing in time along solutions of the space-homogeneous Boltzmann equation for a large class of collision kernels covering all classical interactions derived from systems of particles. For general collision kernels, a sufficient condition for the monotonicity of the Fisher information along the flow is related to the best constant for an integro-differential inequality for functions on the sphere, which belongs in the family of the Log-Sobolev inequalities. As a consequence, we establish the existence of global smooth solutions to the space-homogeneous Boltzmann equation in the main situation of interest where this was not known, namely the regime of very soft potentials. Joint work with Luis Silvestre and Cédric Villani.
›10:30 (30min)
10:30 - 11:00 (30min)
Pause café
›11:00 (1h)
Angeliki Menegaki
In this talk we consider the four-waves spatially homogeneous kinetic equation arising in weak wave turbulence theory from the microscopic Fermi-Pasta-Ulam-Tsingou (FPUT) oscillator chains. This equation is sometimes referred to as the Phonon Boltzmann Equation. I will discuss the global existence and stability of solutions of the kinetic equation near the Rayleigh-Jeans (RJ) thermodynamic equilibrium solutions. This is a joint work with Pierre Germain (Imperial College London) and Joonhyun La (KIAS).
Stability of Rayleigh-Jeans equilibria in the kinetic FPUT equation.
In this talk we consider the four-waves spatially homogeneous kinetic equation arising in weak wave turbulence theory from the microscopic Fermi-Pasta-Ulam-Tsingou (FPUT) oscillator chains. This equation is sometimes referred to as the Phonon Boltzmann Equation. I will discuss the global existence and stability of solutions of the kinetic equation near the Rayleigh-Jeans (RJ) thermodynamic equilibrium solutions. This is a joint work with Pierre Germain (Imperial College London) and Joonhyun La (KIAS).
11:00 - 12:00 (1h)
Angeliki Menegaki
Stability of Rayleigh-Jeans equilibria in the kinetic FPUT equation.
In this talk we consider the four-waves spatially homogeneous kinetic equation arising in weak wave turbulence theory from the microscopic Fermi-Pasta-Ulam-Tsingou (FPUT) oscillator chains. This equation is sometimes referred to as the Phonon Boltzmann Equation. I will discuss the global existence and stability of solutions of the kinetic equation near the Rayleigh-Jeans (RJ) thermodynamic equilibrium solutions. This is a joint work with Pierre Germain (Imperial College London) and Joonhyun La (KIAS).
›12:15 (1h45)
12:15 - 14:00 (1h45)
Déjeuner
›15:00 (1h)
Andreia Chapouto
The intermediate long wave equation (ILW) models the internal wave propagation of the interface in a stratified fluid of finite depth, providing a natural connection between the deep-water regime (= the BO regime) and the shallow-water regime (= the KdV regime). Exploiting the complete integrability of ILW, I will discuss the statistical convergence of ILW to both BO and KdV, namely the convergence of the higher order conservation laws for ILW and their associated invariant measures. In particular, as KdV possesses only half as many conservation laws as ILW and BO, we observe a novel 2-to-1 collapse of ILW conservation laws to those of KdV, which yields alternative modes of convergence for the associated measures in the shallow-water regime. This talk is based on joint work with Guopeng Li and Tadahiro Oh.
Deep- and shallow-water limits of statistical equilibria for the intermediate long wave equation.
The intermediate long wave equation (ILW) models the internal wave propagation of the interface in a stratified fluid of finite depth, providing a natural connection between the deep-water regime (= the BO regime) and the shallow-water regime (= the KdV regime). Exploiting the complete integrability of ILW, I will discuss the statistical convergence of ILW to both BO and KdV, namely the convergence of the higher order conservation laws for ILW and their associated invariant measures. In particular, as KdV possesses only half as many conservation laws as ILW and BO, we observe a novel 2-to-1 collapse of ILW conservation laws to those of KdV, which yields alternative modes of convergence for the associated measures in the shallow-water regime. This talk is based on joint work with Guopeng Li and Tadahiro Oh.
15:00 - 16:00 (1h)
Andreia Chapouto
Deep- and shallow-water limits of statistical equilibria for the intermediate long wave equation.
The intermediate long wave equation (ILW) models the internal wave propagation of the interface in a stratified fluid of finite depth, providing a natural connection between the deep-water regime (= the BO regime) and the shallow-water regime (= the KdV regime). Exploiting the complete integrability of ILW, I will discuss the statistical convergence of ILW to both BO and KdV, namely the convergence of the higher order conservation laws for ILW and their associated invariant measures. In particular, as KdV possesses only half as many conservation laws as ILW and BO, we observe a novel 2-to-1 collapse of ILW conservation laws to those of KdV, which yields alternative modes of convergence for the associated measures in the shallow-water regime. This talk is based on joint work with Guopeng Li and Tadahiro Oh.
›16:00 (30min)
16:00 - 16:30 (30min)
Pause café
›16:30 (1h)
Camille Laurent
In this talk, I will first present the known results of unique continuation for wave-like equations. I will explain the difficulties of obtaining global results under natural geometrical assumptions. Then, I will present a recent result, in collaboration with Cristobal Loyola, where we prove unique continuation for semilinear wave equations under the geometric control assumption. A crucial step is the global propagation of analyticity in time from open sets verifying the geometric control condition. The proof uses control methods associated with Hale-Raugel ideas concerning attractor regularity.
Propagation of global analyticity and unique continuation for semilinear wave equations.
In this talk, I will first present the known results of unique continuation for wave-like equations. I will explain the difficulties of obtaining global results under natural geometrical assumptions. Then, I will present a recent result, in collaboration with Cristobal Loyola, where we prove unique continuation for semilinear wave equations under the geometric control assumption. A crucial step is the global propagation of analyticity in time from open sets verifying the geometric control condition. The proof uses control methods associated with Hale-Raugel ideas concerning attractor regularity.
16:30 - 17:30 (1h)
Camille Laurent
Propagation of global analyticity and unique continuation for semilinear wave equations.
In this talk, I will first present the known results of unique continuation for wave-like equations. I will explain the difficulties of obtaining global results under natural geometrical assumptions. Then, I will present a recent result, in collaboration with Cristobal Loyola, where we prove unique continuation for semilinear wave equations under the geometric control assumption. A crucial step is the global propagation of analyticity in time from open sets verifying the geometric control condition. The proof uses control methods associated with Hale-Raugel ideas concerning attractor regularity.
17:30 - 18:30 (1h)
Luc Robbiano
Observation of the Stokes system for general boundary condition.
TBA.
›19:30 (1h30)
19:30 - 21:00 (1h30)
Dîner
