We consider the Kuramoto–Sivashinsky equation (KSE) on the two-dimensional torus in the presence of advection by a given background shear flow. Under the assumption that the shear has a finite number of critical points and there are linearly growing modes only in the direction of the shear, we prove global existence of solutions with data in L2, using a bootstrap argument. The initial data can be taken arbitrarily large.
All Science Journal Classification (ASJC) codes
- Mathematics (miscellaneous)