For the second installment of this series of posts (which started here) on the first Bourbaki seminar of 2015, we will discuss Gilles Carron… 2,384 more words

## Tags » Math.AP

#### Discretised wave equations

The wave equation is usually expressed in the form

where is a function of both time and space , with being the Laplacian operator. One can generalise this equation in a number of ways, for instance by replacing the spatial domain with some other manifold and replacing the Laplacian with the Laplace-Beltrami operator or adding lower order terms (such as a potential, or a coupling with a magnetic field). 1,149 more words

#### Kolmogorov's power law for turbulence

Many fluid equations are expected to exhibit turbulence in their solutions, in which a significant portion of their energy ends up in high frequency modes. A typical example arises from the three-dimensional periodic… 940 more words

#### Conserved quantities for the surface quasi-geostrophic equation

As in the previous post, all computations here are at the formal level only.

In the previous blog post, the Euler equations for inviscid incompressible fluid flow… 697 more words