Stochastic Lagrangian Path for Leray's Solutions of 3D Navier-Stokes Equations

Zhang X, Zhao G (2020)
Communications in Mathematical Physics.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch

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Autor*in
Zhang, Xicheng; Zhao, GuohuanUniBi
Einrichtung
Abstract / Bemerkung
In this paper we show the existence of stochastic Lagrangian particle trajectory for Leray's solution of 3D Navier-Stokes equations. More precisely, for any Leray's solution u of 3D-NSE and each (s, x) is an element of R+ x R-3, we show the existence of weak solutions to the following SDE, which have densities rho(s, x) (t, y) belonging to H-q(1, p) with p, q is an element of [1, 2) and 3/p + 2/q > 4: dX(s, t) = u(s, X-s,X- t)dt + root 2 nu dW(t), X-s,X- s = x, t >= s, where W is a three dimensional standard Brownian motion, nu > 0 is the viscosity constant. Moreover, we also showthat for Lebesgue almost all (s, x), the solution X-s(n),. (x) of the above SDE associated with the mollifying velocity field un weakly converges to X-s, . ( x) so that X is a Markov process in almost sure sense.
Erscheinungsjahr
2020
Zeitschriftentitel
Communications in Mathematical Physics
ISSN
0010-3616
eISSN
1432-0916
Page URI
https://pub.uni-bielefeld.de/record/2949196

Zitieren

Zhang X, Zhao G. Stochastic Lagrangian Path for Leray's Solutions of 3D Navier-Stokes Equations. Communications in Mathematical Physics. 2020.
Zhang, X., & Zhao, G. (2020). Stochastic Lagrangian Path for Leray's Solutions of 3D Navier-Stokes Equations. Communications in Mathematical Physics. doi:10.1007/s00220-020-03888-w
Zhang, X., and Zhao, G. (2020). Stochastic Lagrangian Path for Leray's Solutions of 3D Navier-Stokes Equations. Communications in Mathematical Physics.
Zhang, X., & Zhao, G., 2020. Stochastic Lagrangian Path for Leray's Solutions of 3D Navier-Stokes Equations. Communications in Mathematical Physics.
X. Zhang and G. Zhao, “Stochastic Lagrangian Path for Leray's Solutions of 3D Navier-Stokes Equations”, Communications in Mathematical Physics, 2020.
Zhang, X., Zhao, G.: Stochastic Lagrangian Path for Leray's Solutions of 3D Navier-Stokes Equations. Communications in Mathematical Physics. (2020).
Zhang, Xicheng, and Zhao, Guohuan. “Stochastic Lagrangian Path for Leray's Solutions of 3D Navier-Stokes Equations”. Communications in Mathematical Physics (2020).

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