On Stochastic Euler equation in $\mathbb{R}^d$
G. Valiukevicius (Vilnius University)
Abstract
Following the Arnold-Marsden-Ebin approach, we prove local (global in 2-D) existence and uniqueness of classical (Hölder class) solutions of stochastic Euler equation with random forcing.
Full Text: Download PDF | View PDF online (requires PDF plugin)
Pages: 1-20
Publication Date: February 17, 2000
DOI: 10.1214/EJP.v5-62
References
- S. V. Arnold, Sur la geometrie differentielle des groupes de Lie de dimension infinie et ses applications a l'hydrodynamic des fluides parfaits, Ann. Inst. Grenoble, 16 (1966), 319-361. Math Review link
- D. G. Ebin and J. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math., 92 (1970), 102-163. Math Review link
- D. G. Ebin, A concise presentation of the Euler equation of hydrodynamics, Comm. in Partial Diff. Equations, 9 (1984), 539-559. Math Review link
- J. Marsden, Applications of global analysis in mathematical physics, Publish or Perish, (1974). Math Review link
- L. Stupelis, Navier-Stokes equations in irregular domains, Kluwer Academic Publishers, Dordrecht, (1995). Math Review link
- D. Gilbarg, N. S. Trudinger, Elliptic partial differential equations of the second order, Springer Verlag, Berlin, (1983). Math Review link
- B. L. Rozovskii, Stochastic Evolution Systems, Kluwer Academic Publishers, Dordrecht, (1990). Math Review link
- R. Mikulevicius and G. Valiukevicius, On stochastic Euler equation, Lithuanian Math. J., 38 (1998), 181-192. Math Review link

This work is licensed under a Creative Commons Attribution 3.0 License.