On the Incompressible Limit for a Tumour Growth Model Incorporating Convective Effects
Explore mathematical modeling of tumor growth with convective effects, focusing on the incompressible limit and its connection to free-boundary problems.
A Multiple Time Renewal Equation for Neural Assemblies with Elapsed Time Model
Explore neural assemblies through a multiple time renewal equation, focusing on the elapsed time model and its implications for understanding brain dynamics.
Fokker-Planck Equations of Neuron Networks: Understanding Time Periodic Solutions
Explore Fokker-Planck equations in neuron networks, focusing on time periodic solutions and their implications for neural dynamics.
The Nonlinear Stability of Black Holes: An Overview
Explore the mathematical properties of black holes, focusing on their stability as solutions to Einstein's equation and recent proof of nonlinear stability for slowly rotating Kerr black holes.
Voigt Boussinesq Equations - Global Regularity and Fluid Dynamics
Explore Voigt Boussinesq equations, their relation to fluid mechanics, and global regularity results for critical cases. Gain insights into incompressible fluid equations and their approximations.
Non-uniqueness in the Partial Differential Equations of Fluid Dynamics
Explore instability and non-uniqueness in fluid dynamics equations, focusing on recent advancements in Euler and Navier-Stokes equations and their implications for unpredictability.
Geometry of Shock Formation and Maximal Development for Euler
Explore the geometry of shock formation and maximal development in Euler equations, focusing on fluid flow analysis and honoring David Ebin's contributions.
Emergent Singular Solutions of Nonlinear Wave Equations
Explore nonlinear wave equations and their emergent singular solutions with Imperial College London's Darryl Holm in this advanced mathematics workshop.
Random Matrices and Statistical Physics - Lecture 2
Explore connections between random matrices and statistical physics, delving into advanced mathematical concepts and their applications in complex systems analysis.
Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 6
Explore modern techniques for analyzing flows of irregular vector fields, with applications to fluid dynamics and turbulence theory. Gain insights into nonlinear PDEs and Euler/Navier-Stokes equations.
Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 5
Explore modern techniques for analyzing flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics PDEs.
Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 4
Explore modern techniques for analyzing flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics PDEs.
Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 3
Explore modern techniques for analyzing flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics PDEs.
Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 2
Explore modern techniques for analyzing flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics PDEs.
Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 1
Explore modern concepts in flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics and turbulence theory.
Probabilistic and Deterministic Scattering for Non-linear Schrödinger Equations
Explore probabilistic and deterministic scattering in non-linear Schrödinger equations, examining random initial data and wave operators through recent research findings.
Mean-Field Limits for Singular Flows
Explore mean-field limits for singular flows, focusing on Coulomb and Riesz interactions in gradient and conservative systems, with insights on convergence methods.
Reversal in the Stationary Prandtl Equations
Explore reversal and recirculation in stationary Prandtl equations, examining the Goldstein singularity and analyzing the system as a quasilinear, mixed-type, free-boundary problem.
Instability and Non-uniqueness for the Euler and Navier-Stokes Equations
Explore recent advances in non-unique solutions for incompressible Navier-Stokes and Euler equations, including groundbreaking work on forced Navier-Stokes equations' non-uniqueness.
The Quartic Integrability and Long Time Existence of Steep Water Waves in 2D
Explore advanced mathematical analysis of 2D water waves, focusing on quartic integrability and long-term existence of steep waves in infinite depth scenarios.
The Nonlinear Stability of Slowly Rotating Kerr Black Holes
Explore nonlinear stability of slowly rotating Kerr black holes through joint research findings, delving into advanced astrophysical concepts and mathematical models.