Stability and uniqueness for a turbulence model of Burgers

Abstract

In his early work on mathematical models of turbulence, J. M. Burgers proposed a nonlinear system, coupling an ordinary and a partial differential equation, to simulate flow in a channel. The now well-known Burgers equation arose in his work from a simplification of this system. The original system has some interesting features not shared by the Burgers equation. This investigation establishes results on the stability of the “laminar” stationary solution and uniqueness of the nonstationary solution of the system.