# 09.12 Incompressible limits (Michael Dreher)

Title: In compressible limits

Speaker: Michael Dreher (Heriot-Watt University Edinburgh)

Time: 09.12.2015, 15:00-16:00

Room: B139

# 26.11 The Self-Organized Hydrodynamics models with density dependent velocity (Hui Yu)

Title: The Self-Organized Hydrodynamics models with density dependent velocity

Speaker: Hui Yu (Aachen)

Abstract: We propose a self-organized hydrodynamics model whose velocity depends on the local density. The analysis shows that the correlation between velocity and the local density is essential to the stability. The results are demonstrated by numerical simulations of the particle and the hydrodynamic models with several experimental functions that define the relation between density and velocity. The growth rate of the unstable modes are analysed among the particle, linearized and nonlinear hydrodynamic models.

Time: 26.11.2015, 14:00-15:00

Room: B6 A302

# 12.11 Discrete Beckner Inequalities via a Bochner-Bakry-Emery Method for Markov Chains (Wen Yue)

Title of talk: Discrete Beckner Inequalities via a Bochner-Bakry-Emery Method for Markov Chains

Speaker: Wen Yue (TU Wien)

Abstract: Beckner inequalities, which interpolate between the logarithmic Sobolev Inequalities and Poincare inequalities, are derived in the context of Markov chains. The proof is based on the Bakry-Emery method and the use of discrete Bochner-type inequalities. We apply our result to several Markov chains including Birth-Death process, Zero-Range process, Bernoulli-Laplace models and Random Transposition models and thus get the exponential convergence rates of the ''distributions'' of these Markov chains to their invariant measures.

Time: 12.11.2015, 14:00-15:00

Room: B6 A302

# 02.11 Derivation of the Vlasov Equation (P. Pickl)

Title: Derivation of the Vlasov Equation

Speaker: Peter Pickl (LMU)

Time: 02.11.2015, 9:30-10:30

Room: TBA

# 29.10 On the diffusion limit of the Boltzmann system for gaseous mixtures (F. Salvarani)

Title: On the diffusion limit of the Boltzmann system for gaseous mixtures.

Speaker: Francesco Salvarani (University of Pavia, Italy and Université Paris-Dauphine, France)

Abstract: In this talk, we consider the non-reactive elastic Boltzmann equation for monatomic gaseous mixtures, and we analyse its behaviour under the standard di ffusive scaling. In particular, we point out the relationships between the cross sections of the model and the diffusion coefficients, emphasizing the differences with respect to the mono-species case.

Time: 29.10.2015, 14:00-15:00

Room: B6 A302

# 17.09 Finite time versus infinite time blowup for a fully parabolic Keller-Segel system (C. Stinner)

Title: Finite time versus infinite time blowup for a fully parabolic Keller-Segel system

Speaker: Christian Stinner (TU Kaiserslautern)

Abstract: Several variants of the Keller-Segel model are used in mathematical biology to describe the evolution of cell populations due to both diffusion and chemotactic movement. In particular, the emergence of cell aggregation is related to blowup of the solution. Critical nonlinearities with respect to the occurrence of blowup had been identified for a quasilinear parabolic-parabolic Keller-Segel system, but it was not known whether the solution blows up in finite or infinite time. We show that indeed both blowup types appear and that the growth of the chemotactic sensitivity function is essential to distinguish between them. We provide conditions for the existence of each blowup type and discuss their optimality. An important ingredient of our proof is a detailed analysis of the Liapunov functional. This is a joint work with T. Cie´slak (Warsaw).

Time: 17.09.2015, 14:00-15:00

Room: B6 A302

# 14.09 Effective one particle equations I (H. Siedentop)

Title: Effective one particle equations I

Speaker: Heinz Siedentop (LMU)

Time: 14.09.2015, 9:30-11:00

Room: A5 C116

# 21.07 Hypocoercivity for a linearized multi-species Boltzmann system (Esther Daus)

Title: Hypocoercivity for a linearized multi-species Boltzmann system

Speaker: Esther Daus (TU Wien)

Abstract: A new coercivity estimate on the spectral gap of the linearized

Boltzmann collision operator for multiple species is proved. The assumptions on the collision kernels include hard and Maxwellian potentials under Grad's angular cut-off condition. Two proofs are given: a non-constructive one, based on the decomposition of the collision operator into a compact and a coercive part, and a constructive one, which exploits the ``cross-effects'' coming from collisions between different species and which yields explicit constants. Furthermore, the essential spectra of the linearized collision operator and the linearized Boltzmann operator are calculated. Based on the spectral-gap estimate, the exponential convergence towards global equilibrium with explicit rate is shown for solutions to the linearized multi-species Boltzmann system onthe torus. The convergence is achieved by the interplay between the dissipative collision operator and the conservative transport operator and is proved by using the hypocoercivity method of Mouhot and Neumann.

Time: 21.07.2015, 14:00-15:00

Room: C012

# 09.06 Relaxation für parabolische Systeme gemischter Ordnung (Michael Dreher)

Title: Relaxation für parabolische Systeme gemischter Ordnung

Speaker: Michael Dreher (Heriot-Watt University Edinburgh)

Abstract: Motiviert durch numerische Verfahren betrachten wir die Approximation von parabolischen Problemen gemischter Ordnung, wie sie zum Beispiel bei der Beschreibung von fluiddynamischen Systemen mit Kapillaritäts- oder Quanteneffekten auftreten, durch relaxierte Systeme einheitlicher Ordnung.

Time: 09.06.2015, 14:00-15:00

Room: B143

# 05.05 Blowup mechanism of 2D Smoluchowski-Poisson equation: in infinite time quantization and finite time simplicity (Suzuki)

Title: Blowup mechanism of 2D Smoluchowski-Poisson equation: in infinite time quantization and finite time simplicity

Speaker: T. Suzuki (Osaka)

Abstract: The Smoluchowski-Poisson equation was formulated by Sire and Chavanis in the study of Brownian particles, where the variational structure matches the scaling invariance. We show that the blowup in infinite time occurs only when the initial total mass is so quantized as 8\pi times integer. Thus we meet the quantized blowup mechanism of this model in three phases; stationary, finite time, and infinite time. From the argument, simplicity of the collapse formed in finite time is proven. The Kantorovich-Rubinstein metric takes a role in accordance with the improved Trudinger-Moser inequality.

Time: 05.05.2015, 14:00-15:00

Room: C116

# 25.03 Low-dimensional structures of stochastic partial Adaptive methods for exploring differential equations (Z. Zhang)

Title: Low-dimensional structures of stochastic partial Adaptive methods for exploring differential equations

Speaker: Zhiwen Zhang (UCLA)

Time: 25.03.2015 14:00-15:00

Room: B139