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Energy dissipation and self-similar solutions for an unforced inviscid dyadic model
D. Barbato, F. Flandoli, F. Morandin
A shell-type model of an inviscid fluid, previously considered in the literature, is investigated in absence of external force. Energy dissipation of positive solutions is proved a…
Uniqueness results for convex Hamilton-Jacobi equations under growth conditions on data
Francesca Da Lio, Olivier Ley
Unbounded stochastic control problems may lead to Hamilton-Jacobi-Bellman equations whose Hamiltonians are not always defined, especially when the diffusion term is unbounded with…
The Kolmogorov operator associated to a Burgers SPDE in spaces of continuous functions
Luigi Manca
We are concerned with a viscous Burgers equation forced by a perturbation of white noise type. We study the corresponding transition semigroup in a space of continuous functions we…
Partial Regularity for Stationary Solutions to Liouville-Type Equation in dimension 3
Francesca Da Lio
In dimension , we prove that the singular set of any stationary solution to the Liouville equation , which belongs to , has Hausdorff dimension at most 1.