The Simons Semester CrossFields PDEs is directed to partial differential equations arising from different areas of sciences, specific problems are often effects of cross fields studies. The semester will run from December 2016 till March 2017 and will focus on the following issues:

  • Weak and measure-valued solutions for Euler system and other systems of hyperbolic conservation laws (method of convex integration, problems of weak-strong uniqueness, Young measures),
  • Existence and regularity of solutions to Navier-Stokes equations (Lagrangian coordinates, Fourier analysis, compensated compactness),
  • Multi-scale flows (complex systems coupling Navier-Stokes/Euler system with other equations, e.g. Fokker-Planck),
  • Models reduction (singular limits in fluid mechanics and homogenization),
  • Kinetic theory (application of kinetic theory in mechanics of fluids and gases - Boltzmann equation, kinetic models in mathematical biology),
Historically, all above models originate form classical gas and fluid mechanics. However, nowadays science: medicine, biology, economics require support by models of above type. We would like to pay our attention on aspects of regularity of constructed solutions, both weak and strong ones. This is a first step to more delicate qualitative analysis of solutions as well as to create effective numerical schemes. The choice of our partners and collaborators will guarantee that the realization of our project will effect on creation of several scientific projects at the top mainstream worldwide level.