Finite-time singularity formation for scalar stretching equations

We consider equations of the type: (Formula presented) , for general linear operators R in any spatial dimension. We prove that such equations almost always exhibit finite-time singularities for smooth and localised solutions. Singularities can even form in settings where solutions dissipate an energy. Such equations arise naturally as models in various physical settings such as inviscid and complex fluids.

Duke Scholars

Author Tarek M Elgindi Mathematics