An Integral Equation Method for the Solution of the Burgers Equation

We consider the Burgers equation in the plane without external forces. It is known that for suitable initial data the corresponding complex solution has singularities at finite time [6]. The numerical solution of this equation can be seen as a first step in the study of the well-known problem of understanding the solutions of Navier-Stokes equations. The numerical solution of the Burgers equation is computed by using a proper integral equation. We describe the results obtained with this numerical method, and some possible extensions of the proposed method to deal with more practical problems.