@article{SLSEDP_2015-2016____A6_0,
author = {Oh, Tadahiro and Tzvetkov, Nikolay},
title = {On the transport of {Gaussian} measures under the flow of {Hamiltonian} {PDEs}},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:6},
pages = {1--9},
publisher = {Institut des hautes des scientifiques & Centre de mathtiques Laurent Schwartz, ole polytechnique},
year = {2015-2016},
doi = {10.5802/slsedp.84},
language = {en},
url = {http://www.numdam.org/articles/10.5802/slsedp.84/}
}
TY - JOUR AU - Oh, Tadahiro AU - Tzvetkov, Nikolay TI - On the transport of Gaussian measures under the flow of Hamiltonian PDEs JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:6 PY - 2015-2016 SP - 1 EP - 9 PB - Institut des hautes des scientifiques & Centre de mathtiques Laurent Schwartz, ole polytechnique UR - http://www.numdam.org/articles/10.5802/slsedp.84/ DO - 10.5802/slsedp.84 LA - en ID - SLSEDP_2015-2016____A6_0 ER -
%0 Journal Article %A Oh, Tadahiro %A Tzvetkov, Nikolay %T On the transport of Gaussian measures under the flow of Hamiltonian PDEs %J Séminaire Laurent Schwartz — EDP et applications %Z talk:6 %D 2015-2016 %P 1-9 %I Institut des hautes des scientifiques & Centre de mathtiques Laurent Schwartz, ole polytechnique %U http://www.numdam.org/articles/10.5802/slsedp.84/ %R 10.5802/slsedp.84 %G en %F SLSEDP_2015-2016____A6_0
Oh, Tadahiro; Tzvetkov, Nikolay. On the transport of Gaussian measures under the flow of Hamiltonian PDEs. Séminaire Laurent Schwartz — EDP et applications (2015-2016), Exposé no. 6, 9 p. doi : 10.5802/slsedp.84. http://www.numdam.org/articles/10.5802/slsedp.84/
[1] J. Bourgain, Periodic nonlinear Schrödinger equation and invariant measures, Comm. Math. Phys. 166 (1994), no. 1, 1–26.
[2] R. Cameron, W. Martin, Transformations of Wiener integrals under translations, Ann. of Math. (2) 45, (1944). 386–396.
[3] A.B. Cruzeiro, Équations différentielles ordinaires: non explosion et mesures quasi-invariantes, (French) J. Funct. Anal. 54 (1983), no. 2, 193–205.
[4] Y. Deng, N. Tzvetkov, N. Visciglia, Invariant measures and long time behaviour for the Benjamin-Ono equation III, Comm. Math. Phys. 339 (2015), no. 3, 815–857.
[5] A. Nahmod, L. Rey-Bellet, S. Sheffield, G. Staffilani, Absolute continuity of Brownian bridges under certain gauge transformations, Math. Res. Lett. 18 (2011), no. 5, 875–887.
[6] T. Oh, Invariance of the white noise for KdV, Comm. Math. Phys. 292 (2009), no. 1, 217–236.
[7] T. Oh, N. Tzvetkov, Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrdinger equation, . | arXiv
[8] J. Quastel, B. Valkó, KdV preserves white noise, Comm. Math. Phys. 277 (2008), no. 3, 707–714.
[9] R. Ramer, On nonlinear transformations of Gaussian measures, J. Functional Analysis 15 (1974), 166–187.
[10] N. Tzvetkov, Quasi-invariant Gaussian measures for one dimensional Hamiltonian PDE’s, Forum Math. Sigma 3 (2015), e28, 35 pp.
[11] N. Tzvetkov, N. Visciglia, Invariant measures and long-time behavior for the Benjamin-Ono equation, Int. Math. Res. Not. IMRN 2014, no. 17, 4679–4714.
[12] N. Tzvetkov, N. Visciglia, Invariant measures and long time behaviour for the Benjamin-Ono equation II, J. Math. Pures Appl. (9) 103 (2015), no. 1, 102–141.
[13] V. Yudovich, Non-stationary flows of an ideal incompressible fluid, Zh. Vychisl. Math. i Math. Fiz. (1963) 1032–1066 (1963) (in Russian).
[14] P. Zhidkov, On an infinite sequence of invariant measures for the cubic nonlinear Schrödinger equation, Int. J. Math. Math. Sci. 28 (2001), no. 7, 375–394.
[15] P. Zhidkov, Korteweg-de Vries and nonlinear Schrödinger equations: qualitative theory, Lecture Notes in Mathematics, 1756. Springer-Verlag, Berlin, 2001. vi+147 pp.
Cité par Sources :
