Active scalars and the Euler equations
Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation
Hölder continuity of solutions of supercritical dissipative hydrodynamic transport equations
Non-planar fronts in Boussinesq reactive flows
Existence of pulsating waves in a model of flames in sprays
A one-dimensional system describing the propagation of low Mach number flames in sprays is studied. We show that pulsating waves may exist when the droplet distribution in the unburnt region is spatially periodic. The range of possible propagation speeds may be either bounded or unbounded, depending on the threshold temperatures of the burning and vaporization rates.
On the global existence for the Muskat problem
The Muskat problem models the dynamics of the interface between two incompressible immiscible fluids with different constant densities. In this work we prove three results. First we prove an maximum principle, in the form of a new “log” conservation law which is satisfied by the equation (1) for the interface. Our second result is a proof of global existence for unique strong solutions if the initial data is smaller than an explicitly computable constant, for instance . Previous results of this...
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