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The Schauder estimate for kinetic integral equations
Cyril Imbert, Luis Silvestre
We establish interior Schauder estimates for kinetic equations with integro-differential diffusion. We study equations of the form ,…
Multi-dimensional Burgers equation with unbounded initial data: well-posedness and dispersive estimates
Denis Serre, Luis Silvestre
The Cauchy problem for a scalar conservation laws admits a unique entropy solution when the data is a bounded measurable function (Kruzhkov). The semi-group i…
A dispersive estimate for the multidimensional Burgers equation
Luis Silvestre
We study the multi-dimensional Burgers equation . We prove that the norm of entropy solutions of this equation decays polynomi…
Decay estimates for large velocities in the Boltzmann equation without cutoff
Cyril Imbert, Clément Mouhot, Luis Silvestre
We consider solutions to the full (spatially inhomogeneous) Boltzmann equation with periodic spatial conditions , for hard and moderately soft poten…