4 citations · 10 across the 15 of their papers we have counts for
15 papers
Ekman Boundary Layers Under Transport Noise
Daniel Goodair, Szymon Sobczak
We consider a 3D rotating Navier-Stokes equation with transport-stretching noise, posed between two horizontal plates, and study the joint limit of vanishing vertical viscosity and…
Global well-posedness for the 2D stochastic hypoviscous Navier-Stokes equations
Daniel Goodair, Floris Roodenburg
We study stochastic hypoviscous Navier--Stokes equations on the torus with dissipation for and multiplicative noise. Relying on stochastic maximal r…
Anisotropic Inviscid Limit for the Navier-Stokes Equations with Transport Noise Between Two Plates
Daniel Goodair
We investigate an anisotropic vanishing viscosity limit of the 3D stochastic Navier-Stokes equations posed between two horizontal plates, with Dirichlet no-slip boundary condition.…
Itô-Stratonovich Conversion in Infinite Dimensions for Unbounded, Time-Dependent, Nonlinear Operators
Daniel Goodair
We prove that a solution, in a variational framework, to the Stratonovich stochastic partial differential equation with noise is given by a soluti…
Closed Estimates of Leray Projected Transport Noise and Strong Solutions of the Stochastic Euler Equations
Daniel Goodair
We consider the incompressible Euler and Navier-Stokes equations on the three dimensional torus, in velocity form, perturbed by a transport or transport-stretching Stratonovich noi…
Infinite Boundary Friction Limit for Weak Solutions of the Stochastic Navier-Stokes Equations
Daniel Goodair
We address convergence of the unique weak solutions of the 2D stochastic Navier-Stokes equations with Navier boundary conditions, as the boundary friction is taken uniformly to inf…
High Order Smoothness for Stochastic Navier-Stokes Equations with Transport and Stretching Noise on Bounded Domains
Daniel Goodair
We obtain energy estimates for a transport and stretching noise under Leray Projection on a 2D bounded convex domain, in Sobolev Spaces of arbitrarily high order. The estimates are…
Improved Blow-Up Criterion in a Variational Framework for Nonlinear SPDEs
Daniel Goodair
We extend recent existence and uniqueness results for maximal solutions of SPDEs through an improved blow-up criterion. Whilst the maximal time of existence is typically characteri…
Weak and Strong Solutions to Nonlinear SPDEs with Unbounded Noise
Daniel Goodair
We introduce an extended variational framework for nonlinear SPDEs with unbounded noise, defining three different solution types of increasing strength along with criteria to estab…
Navier-Stokes Equations with Navier Boundary Conditions and Stochastic Lie Transport: Well-Posedness and Inviscid Limit
Daniel Goodair
We prove the existence and uniqueness of global, probabilistically strong, analytically strong solutions of the 2D Stochastic Navier-Stokes Equation under Navier boundary condition…
The Zero Viscosity Limit of Stochastic Navier-Stokes Flows
Daniel Goodair, Dan Crisan
We introduce an analogue to Kato's Criterion regarding the inviscid convergence of stochastic Navier-Stokes flows to the strong solution of the deterministic Euler equation. Our as…
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…