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Measures on Hilbert spaces and applications to hydrodynamics
(University of Missouri--Columbia, 2010)
Homogeneous and isotropic statistical solutions of the Navier-Stokes equations are produced. These are shown to be approximated by Galyerkin statistical solutions on finite dimensional subspaces. Homogeneous and isotropic ...
Stochastically perturbed Navier-Stokes system on the rotating sphere
(University of Missouri--Columbia, 2013)
We show the existence and uniqueness of an invariant measure for the kick-forced Navier-Stokes system on the 2-dimensional sphere, first without deterministic force and then with a time-independent deterministic force. The ...
Statistical and stochastic results for three dimensional fluids
(University of Missouri--Columbia, 2012)
In part I, we show that the longitudinal correlation function for homogeneous and isotropic turbulence remains negative in an interval of time, up to Galerkin approximation. Part II covers the existence and uniqueness of ...
Limit of many molecules dynamics with rigorous macroscopic results
(University of Missouri--Columbia, 2013)
The thesis builds on recent ideas that combine work by C.B. Morrey (1955) and D.W. Jepsen & D. ter Haar (1962) with more recent analytic techniques: measure disintegration, PDEs for measures, etc. (M.I. Vishik & A.V. ...