# Differential equations of Mathematical Physics

Differential equations are an extremely important tool in natural sciences. Since Newton, they have been extensively used to model physical systems and to make predictions about their equilibrium and non-equilibrium properties. At the same time, differential equations define a very active area of mathematics, with a large scientific community working towards the solution of famous and challenging conjectures. It is therefore not surprising that differential equations play an important role in mathematical physics and, in particular, in SwissMAP.

Among the topics studied in this research direction are:

- dynamical system and chaos (ordinary differential equations)
- kinetic theory (Boltzmann equation)
- fluid dynamics (Euler, Navier-Stokes equations)
- quantum mechanics (Schrödinger equation)
- general relativity (Einstein equation)