Thursday, June 5, 2014 - 14:00
Aula 1B1 Stochastic Equations in Hydrodynamics
Wladimir Neves Universidade Federal do Rio de Janeiro
We present some results concerning stochastic linear transport equations and
quasilinear scalar conservation laws, where the additive noise is a perturbation
of the drift. Due to the introduction of the stochastic term, we may prove for instance well-posedness for continuity equation (divergence-free), Cauchy problem, meanwhile uniqueness may fail for the deterministic case, see ,  and . Also for the transport equation, Dirichlet data, we established a better trace result by the introduction of the noise, see .
We introduce the study of stochastic hyperbolic conservation laws,
in a different direction of , applying the kinetic-semigroup theory.
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with Ladyzhenskaya-Prodi-Serrin condition, arXiv:1307.6484v1, 2013.
 W. Neves, C .Olivera, Stochastic transport equation
in bounded domains, in preparation.
Joint work with: Christian Olivera (Universidade Estadual de Campinas)