4 citations · 10 across the 15 of their papers we have counts for
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On the Navier-Stokes Equations with Stochastic Lie Transport
Daniel Goodair, Dan Crisan
We prove the existence and uniqueness of maximal solutions to the 3D SALT (Stochastic Advection by Lie Transport, [Holm arXiv:1410.8311]) Navier-Stokes Equation in velocity and vor…
Existence and Uniqueness of Maximal Solutions to SPDEs with Applications to Viscous Fluid Equations
Daniel Goodair, Dan Crisan, Oana Lang
We present two criteria to conclude that a stochastic partial differential equation (SPDE) posseses a unique maximal strong solution. This paper provides the full details of the ab…
Stochastic Calculus in Infinite Dimensions and SPDEs
Daniel Goodair
These notes rigorously construct the stochastic integral of a Hilbert Space valued process driven by a Cylindrical Brownian Motion. We expand upon this stochastic calculus to prese…
Existence and Uniqueness of Maximal Solutions to a 3D Navier-Stokes Equation with Stochastic Lie Transport
Daniel Goodair
We present here a criterion to conclude that an abstract SPDE posseses a unique maximal strong solution, which we apply to a three dimensional Stochastic Navier-Stokes Equation. In…