There will be an invited talk.

Title: Derivation principle of BGK models
Speaker: Prof. Stephane Brull (Univ. of Bordeaux)
Time: 2020 January 14th, 10:30am~11:20pm
Place: 27-116
Abstract:
In this talk we will present a derivation principle of BGK
models using the resolution of an entropy minimization problem.

The construction is based as on the introduction of relaxation
coefficients and a principle of entropy minimization under
constraints for moments. These free parameters are next ajusted to
transport coefficients when performing a Chapman-Engskog expansion
ip to Navier-Stokes. Firstly, the methodology will be explained and
illustrated for a monoatomic and polyatomic single gas.
Next the case of gas mixtures is considered. In this part, after
clarifying the Chapman-Engskog, a BGK model is derived. This BGK
model is proved to satisfy Fick and Newton laws. In a last part, we
will explain how to extend our model to reacting gas mixtures.

There will be an HYKE Intensive Lectures.

Title: HYKE Intensive Lectures on Symmetric Hyperbolic Systems of Balance Laws and State
Lecturers: Prof. Tommaso Ruggeri (Univ. of Bologna)
                   Prof. Masaru Sugiyama (Nagoya Institute of Technology)
Time: 2019 December 3rd, 9:00am~1:00pm
           2019 December 6th, 9:00am~5:00pm
           2019 December 11th, 9:00am~11:00am
Place: 27-116 (3rd), 27-220 (6th, 11th)
Lecture Topics:
Prof. Ruggeri:
Lecture 1,2: Balance Laws, Hyperbolic Systems, Symmetric Systems. Main field and theorem of symmetrization. Examples of Euler fluids, non-linear elasticity, MHD, Born-Infeld nonlinear electrodynamics, relativistic fluids.
Lecture 3,4: Compatibility between Galilean invariance and Entropy Principle. Qualitative analysis, K -condition and global existence of smooth solutions. Principal subsystems and nesting theories with examples. The mixture of gas and connection with Cucker-Smale models.
Lecture 5,6: Shock wave and growth of entropy across the shock, shock structure and sub-shocks formation. Problematic of Rational Extended Thermodynamics in mono and polyatomic gas.
Prof. Sugiyama:
0. Preliminary Discussion
1. Introduction
  1.1 How to describe macroscopic phenomena?
  1.2 Three levels of description of macroscopic systems
2. Equilibrium Statistical Mechanics
  2.1 Distribution function and the Liouville equation
  2.2 Gibbs ensembles
     2.2.1 Microcanonical ensemble, and its application to ideal gas
     2.2.2 Canonical ensemble, and its applications to ideal gas and a system of harmonic oscillators
     2.2.3 Grandcanonical ensemble, and its application to ideal gas
  2.3 Remarks
     2.3.1 Gibbs entropy and information entropy
     2.3.2 Fluctuation
     2.3.3 Validity range of classical statistical mechanics
3. Some Topics I
  3.1 Phase transition
     3.1.1 Virial expansion and the van der Waals equation of state
     3.1.2 Yang and Lee theory of phase transition
     3.1.3 Ising model
     3.1.4 Critical phenomena: Renormalization group approach
  3.2 Fermi statistics and Bose statistics
4. Non-Equilibrium Statistical Mechanics
  4.1 BBGKY hierarchy of the distribution functions
  4.2 Boltzmann equation and the system of moment equations
5. Some Topics II
  5.1 Extended thermodynamics – A new non-equilibrium thermodynamics –
  5.2 Linear response theory
  5.3 Stochastic processes
6. Concluding Remarks and Outlook

There will be an invited talk.

Title: A condition for blow-up solutions to discrete semilinear wave equations on networks
Speaker: Dr. Min-Jun Choi (Seoul National University)
Time: 2019 November 6th, 10:00am~11:00am
Place: 27-220
Abstract:

There will be an invited talk.

Title: Hyper-elastic Ricci Flow
Speaker: Prof. Marshall Slemrod (University of Wisconsin-Madison)
Time: 2019 November 5th, 11:00am~12:00pm
Place: 27-220
Abstract:
In this talk, I will introduce the concept of hyper-elastic Ricci flow. The equation of hyper-elastic Ricci flow amends the classical Ricci flow by the addition of Cauchy stress tensor which itself is derived from the free energy. The main implication of the theory is a uniformization of material behavior which follows from application of a parabolic minimum principle.

There will be an invited talk.

Title: Green’s functions and Well-posedness of Compressible Navier-Stokes equation
Speaker: Prof. Shih-Hsien Yu (National University of Singapore)
Time: 2018 November 13th, 4:00pm~5:00pm
Place: 27-220
Abstract:
A class of decomposition of Green’s functions for the compressilbe Navier-Stokes linearized around a constant state is introduced. The singular structures of the Green’s functions are developed as essential devices to use the nonlinearity directly to covert the 2nd order quasi-linear PDE into a system of zero-th order integral equation with regular integral kernels. The system of integrable equations allows a wider class of functions such as BV solutions. We have shown global existence and well-posedness of the compressible Navier-Stokes equation for isentropic gas with the gas constant γ∈(0,e) in the Lagrangian coordinate for the class of the BV functions and point wise L∞ around a constant state; and the
underline pointwise structure of the solutions is constructed. It is also shown that for the class of BV solution the solution is at most piecewise C2-solution even though the initial data is piecewise C^infty.

There will be an invited talk.

Title: Vlasov-Poisson-Boltzmann system in convex domains
Speaker: Prof. Chanwoo Kim (Univ. of Wisconsin-Madison)
Time: 2018 November 5th, 11:00am~12:00pm
Place: 27-220
Abstract:
We discuss global well-posedness of Vlasov-Poisson-Boltzmann system when the diffuse reflection boundary condition is imposed.

There will be an invited talk.

Title: Self-Organized Hydrodynamic models for nematic alignment and the application to myxobacteria
Speaker: Prof. Hui Yu (Tsinghua University)
Time: 2018 November 1st, 11:00am~11:50am
Place: 27-220
Abstract:
A continuum model for a population of self-propelled particles interacting through nematic alignment is derived from an individual-based model. The methodology consists of introducing a hydrodynamic scaling of the corresponding mean field kinetic equation. The resulting perturbation problem is solved thanks to the concept of generalized collision invariants. It yields a hyperbolic but nonconservative system of equations for the nematic mean direction of the flow and the densities of particles flowing parallel or antiparallel to this mean direction. An application to myxobacteria is presented.