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  • Séminaire Laurent Schwartz — EDP et applications
  • Année 2015-2016
  • Exposé no. 6
  • Suivant
On the transport of Gaussian measures under the flow of Hamiltonian PDEs
Tadahiro Oh1 ; Nikolay Tzvetkov2
1 School of Mathematics The University of Edinburgh and The Maxwell Institute for the Mathematical Sciences James Clerk Maxwell Building The King’s Buildings Peter Guthrie Tait Road Edinburgh EH9 3FD United Kingdom
2 Université de Cergy-Pontoise 2 avenue Adolphe Chauvin 95302 Cergy-Pontoise Cedex France
Séminaire Laurent Schwartz — EDP et applications (2015-2016), Exposé no. 6, 9 p.
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Publié le : 2016-10-12
DOI : 10.5802/slsedp.84
Affiliations des auteurs :
Tadahiro Oh 1 ; Nikolay Tzvetkov 2

1 School of Mathematics The University of Edinburgh and The Maxwell Institute for the Mathematical Sciences James Clerk Maxwell Building The King’s Buildings Peter Guthrie Tait Road Edinburgh EH9 3FD United Kingdom
2 Université de Cergy-Pontoise 2 avenue Adolphe Chauvin 95302 Cergy-Pontoise Cedex France
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@article{SLSEDP_2015-2016____A6_0,
     author = {Tadahiro Oh and Nikolay Tzvetkov},
     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 = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.84/}
}
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PY  - 2015-2016
SP  - 1
EP  - 9
PB  - Institut des hautes des scientifiques & Centre de mathtiques Laurent Schwartz, ole polytechnique
UR  - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.84/
DO  - 10.5802/slsedp.84
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ID  - SLSEDP_2015-2016____A6_0
ER  - 
%0 Journal Article
%A Tadahiro Oh
%A Nikolay Tzvetkov
%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
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%G en
%F SLSEDP_2015-2016____A6_0
Tadahiro Oh; Nikolay Tzvetkov. 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. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.84/
  • Bibliographie
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[2] R. Cameron, W. Martin, Transformations of Wiener integrals under translations, Ann. of Math. (2) 45, (1944). 386–396.

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[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 Schršdinger 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.

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