Euler-Lagrangian approach to stochastic Euler equations in Sobolev Spaces
Resumen
We study a Lagragian formulation (following [1], [2] and [3] ) of the incompressible Euler equations on a domain Td . The Euler equations with transport noise model the flow of an incompressible inviscid fluid and are (classically) formulated in terms of a divergence–free vector field u (i.e. ∇ · u = 0) as follows: X dut + (ut · ∇ut + ∇pt )dt + L∗σk ut ◦ dWtk = 0 k [...]
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Peter Constantin. “An Eulerian-Lagrangian approach to the Navier-Stokes equations”. Em: Communications in Mathematical Physics 3 (2001), pp. 663–686. doi: 10.1007/s002200000349.
Franco Flandoli. Random perturbation of PDEs and fluid dynamic models. École d’Été de Probabilités de Saint-Flour. Berlin: Springer-verlag, 2011. isbn: 978-3-642-18230-3; 978-3-642-18231-0.
Benjamin C. Pooley e James C. Robinson. “An Eulerian-Lagrangian form for the Euler equations in Sobolev spaces”. Em: Journal of Mathematical Fluid Mechanics 4 (2016), pp. 783–794. doi: 10.1007/s00021-016-0271-8.
Diego Alonso-Orán, Aythami Bethencourt de León, Darryl D. Holm e So Takao. “Modelling the climate and weather of a 2D Lagrangian-averaged Euler-Boussinesq equation with transport noise”. Em: Journal of Statistical Physics 5-6 (2020), pp. 1267–1303. doi:10.1007/s10955-019-02443-9.
G. Falkovich, K. Gawdzki e M. Vergassola. “Particles and fields in fluid turbulence”. Em: Reviews of Modern Physics 4 (2001), pp. 913–975. doi: 10.1103/RevModPhys.73.913.
Franco Flandoli e Dejun Luo. “Euler-Lagrangian approach to 3D stochastic Euler equations”. Em: Journal of Geometric Mechanics 2 (2019), pp. 153–165. doi: 10.3934/jgm.2019008.
Franco Flandoli e Christian Olivera. “Well-posedness of the vector advection equations by stochastic perturbation”. Em: Journal of Evolution Equations 2 (2018), pp. 277–301. doi: 10.1007/s00028-017-0401-7.
Peter Constantin e Gautam Iyer. “A stochastic Lagrangian representation of the three-dimensional incompressible Navier-Stokes equations”. Em: Communications on Pure and Applied Mathematics 3 (2008), pp. 330–345. doi: 10.1002/cpa.20192.
D. Besse. “Stochastic Lagrangian perturbation of Lie transport and applications to fluids”. Em: Nonlinear Analysis 232 (2023), pp. 113–249. doi: 10.1016/j.na.2023.113249.
Diego S. Ledesma. “A local solution to the Navier-Stokes equations on manifolds via stochastic representation”. Em: Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods (2020), p. 8. doi: 10.1016/j.na.2020.111927.
Christian Olivera. “Probabilistic representation for mild solution of the Navier-Stokes equations”. Em: Mathematical Research Letters 28 (2021), pp. 563–573. doi: 10.4310/MRL.2021.v28.n2.a8.
