A case of combined planar Couette-Poiseuille flow corresponding to vanishing horizontal flux has been generalized by the introduction of a model for the surface velocity gradient. A relation corresponding to the Orr-Sommerfeld equation has been derived for this model. The critical value of the surface velocity gradient has been obtained. At the critical point, the corresponding critical Reynold...

A first-principles method to calculate the critical temperature gradient for onset of ion-temperature-gradient mode (ITG) in linear gyrokinetics is presented. We find that conventional notions connection length previously invoked tokamak research should be revised and replaced by a generalized correlation explain this stellarators. Simple numerical experiments gyrokinetic theory show localized ...

We obtain a priori interior Hessian and gradient estimates for special Lagrangian equations with phase larger than a critical value in dimension three. Gradient estimates are also derived for critical and super critical phases in general dimensions.

We obtain a priori interior Hessian and gradient estimates for special Lagrangian equations with phase larger than a critical value in dimension three. Gradient estimates are also derived for critical and super critical phases in general dimensions.