This paper is concerned with the stability problem of the convection roll solutions of the Oberbeck-Boussinesq equations. We consider the stability of the roll solutions with respect to the two-dimensional disturbances. The Eckhaus criterion for the stability and instability of the roll solutions is derived in a mathematically rigorous way.
All Science Journal Classification (ASJC) codes
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics