Boltzmann Equation Courses and Certifications

International Mathematical Union

Convergence of a Dilute Gas to the Fluctuating Boltzmann Equation

Explore the convergence of a dilute gas to the fluctuating Boltzmann equation, examining empirical measure fluctuations and their convergence to a Gaussian process for short and long time periods.

• YouTube
• 48 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Homoenergetic Solutions for the Boltzmann Equation

Explore homoenergetic solutions of the Boltzmann equation, their well-posedness theory, and unique long-time asymptotics in nonequilibrium gas dynamics under shear, expansion, or compression.

• YouTube
• 1 hour
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Deterministic Solution of the Boltzmann Equation - Fast Spectral Methods

Explore fast Fourier spectral methods for solving the Boltzmann equation, addressing computational challenges and showcasing applications in rarefied gas dynamics.

• YouTube
• 40 minutes
• On-Demand
• Free Video

Centre International de Rencontres Mathématiques

Construction of Boltzmann and McKean Vlasov Type Flows - The Sewing Lemma Approach

Explore construction of Boltzmann and McKean Vlasov flows using the sewing lemma approach. Gain insights into stochastic analysis and numerical probability from expert Vlad Bally.

• YouTube
• 43 minutes
• On-Demand
• Free Video

BIMSA

3D Kinetic Couette Flow via the Boltzmann Equation in the Diffusive Limit

Explore the rigorous connection between incompressible Couette flow and the Boltzmann equation through novel anisotropic estimates in the Wiener algebra function space.

• YouTube
• 53 minutes
• On-Demand
• Free Video

Nano-to-Macro Transport Processes

2 reviews

In this course you will learn parallel treatments of photons, electrons, phonons, and molecules as energy carriers, aiming at fundamental understanding and descriptive tools for energy and heat transport processes from nanoscale continuously to macroscal…

• MIT OpenCourseWare
• 34 hours
• On-Demand
• Free Video

Non-Equilibrium Applications of Statistical Thermodynamics

83 ratings at Coursera

Explore transport in gases, spectroscopic methods for thermodynamic analysis, and chemical kinetics with focus on combustion. Gain practical skills in determining properties and using computational tools.

• Coursera
• 7 hours 41 minutes
• On-Demand
• Free Online Course (Audit)

NPTEL;  IIT Madras

Physics - Nonequilibrium Statistical Mechanics

Explore advanced concepts in nonequilibrium statistical mechanics, including Langevin models, linear response theory, Fokker-Planck equations, and critical phenomena, with practical applications and quizzes.

• YouTube
• 1 day 9 hours
• On-Demand
• Free Video

Society for Industrial and Applied Mathematics

Gaussian Lower Bounds for the Boltzmann Equation Without Cut-off - SIAM PDE Seminar

Explore Gaussian lower bounds for the Boltzmann equation, examining particle density evolution in gases and conditional estimates for solving global well-posedness challenges in fluid dynamics.

• YouTube
• 1 hour
• On-Demand
• Free Video

Society for Industrial and Applied Mathematics

From Newton to Boltzmann - Fluctuations and Large Deviations in Hard Sphere Gas Dynamics

Explore macroscopic fluctuations in hard sphere gases, including deviations from the Boltzmann equation, central limit theorem, and large deviation bounds in the Boltzmann-Grad limit.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

ICTP Mathematics

Construction of Weak Solutions for the Landau Equation by Approximations of Solutions to

Explore the construction of weak solutions for the Landau equation through approximations of Boltzmann equation solutions in grazing collision limit scenarios.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

ICTP Mathematics

Regularity of the Boltzmann Equation in Bounded Domains - I

Explore the regularity of the Boltzmann equation in bounded domains, focusing on advanced mathematical concepts and applications in geometry, physics, and probability theory.

• YouTube
• 56 minutes
• On-Demand
• Free Video

ICTP Mathematics

Regularity of the Boltzmann Equation in Bounded Domains - II

Explore advanced mathematical concepts in nonlocal PDEs, focusing on the Boltzmann equation's regularity in bounded domains. Gain insights from expert Tonon, D. in this in-depth lecture.

• YouTube
• 49 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

On a Multi-Species Kinetic Model of Plasma, Theory and Numerics

Explore a new multi-species kinetic model for plasma, examining its theoretical properties and numerical solutions in the context of inertial confinement fusion.

• YouTube
• 51 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Scaling Limits and Effective Equations in Kinetic Theory I

Explores scaling limits and effective equations in kinetic theory, focusing on Boltzmann and Landau equations for rarefied gases and weakly interacting plasmas, discussing mathematical challenges in rigorous derivation.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video