Existence and Uniqueness of Maximal Solutions to a 3D Navier-Stokes Equation with Stochastic Lie Transport
نویسندگان
چکیده
We present here a criterion to conclude that an abstract SPDE posseses unique maximal strong solution, which we apply three dimensional Stochastic Navier-Stokes Equation. Inspired by the work of [Kato and Lai,1984] in deterministic setting, provide comparable result stochastic case whilst facilitating variety noise structures such as additive, multiplicative transport. In particular our is designed fit viscous fluid dynamics models with Advection Lie Transport (SALT) introduced [Holm,2015]. Our application Incompressible equation matches existence uniqueness theory. This short summarises results announces two papers [Goodair et al, 2022] give full details for well-posedness arguments
منابع مشابه
Tamed 3d Navier-stokes Equation: Existence, Uniqueness and Regularity
In this paper, we prove the existence and uniqueness of a smooth solution to a tamed 3D Navier-Stokes equation in the whole space. In particular, if there exists a bounded smooth solution to the classical 3D Navier-Stokes equation, then this solution satisfies our tamed equation. Moreover, using this renomalized equation we can give a new construction for a suitable weak solution of the classic...
متن کاملStochastic Tamed 3d Navier-stokes Equations: Existence, Uniqueness and Ergodicity
In this paper, we prove the existence of a unique strong solution to a stochastic tamed 3D Navier-Stokes equation in the whole space as well as in the periodic boundary case. Then, we also study the Feller property of solutions, and prove the existence of invariant measures for the corresponding Feller semigroup in the case of periodic conditions. Moreover, in the case of periodic boundary and ...
متن کاملUniqueness of Solutions of the Stochastic Navier–stokes Equation with Invariant Measure given by the Enstrophy
A stochastic Navier–Stokes equation with space-time Gaussian white noise is considered, having as infinitesimal invariant measure a Gaussian measure µν whose covariance is given in terms of the enstrophy. Pathwise uniqueness for µν-a.e. initial velocity is proven for solutions having µν as invariant measure. 1. Introduction. We are interested in the stochastic Navier–Stokes equation with a spac...
متن کاملExistence, Uniqueness and Regularity of Stationary Solutions to Inhomogeneous Navier-stokes Equations in R
For a bounded domain Ω ⊂ Rn , n > 3, we use the notion of very weak solutions to obtain a new and large uniqueness class for solutions of the inhomogeneous Navier-Stokes system −∆u + u · ∇u +∇p = f , div u = k, u|∂Ω = g with u ∈ L q , q > n, and very general data classes for f , k, g such that u may have no differentiability property. For smooth data we get a large class of unique and regular s...
متن کاملExistence & Smoothness of the Navier–stokes Equation
Equation (1) is just Newton’s law f = ma for a fluid element subject to the external force f = (fi(x, t))1 i n and to the forces arising from pressure and friction. Equation (2) just says that the fluid is incompressible. For physically reasonable solutions, we want to make sure u(x, t) does now grow large as |x| → ∞. Hence, we will restrict attention to forces f and initial conditions u◦ that ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of planet earth
سال: 2022
ISSN: ['2524-4272', '2524-4264']
DOI: https://doi.org/10.1007/978-3-031-18988-3_7