@article{SEDP_1997-1998____A24_0, author = {Castella, Fran\c{c}ois}, title = {Effets dispersifs dans les \'equations de {Schr\"odinger} et de {Vlasov}}, journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"}, note = {talk:24}, pages = {1--14}, publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {1997-1998}, zbl = {1061.35517}, mrnumber = {1660537}, language = {fr}, url = {http://www.numdam.org/item/SEDP_1997-1998____A24_0/} }
TY - JOUR AU - Castella, François TI - Effets dispersifs dans les équations de Schrödinger et de Vlasov JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:24 PY - 1997-1998 SP - 1 EP - 14 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/item/SEDP_1997-1998____A24_0/ LA - fr ID - SEDP_1997-1998____A24_0 ER -
%0 Journal Article %A Castella, François %T Effets dispersifs dans les équations de Schrödinger et de Vlasov %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:24 %D 1997-1998 %P 1-14 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://www.numdam.org/item/SEDP_1997-1998____A24_0/ %G fr %F SEDP_1997-1998____A24_0
Castella, François. Effets dispersifs dans les équations de Schrödinger et de Vlasov. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1997-1998), Exposé no. 24, 14 p. http://www.numdam.org/item/SEDP_1997-1998____A24_0/
[Ar] A.Arnold, Self-consistent relaxation-time models in quantum mechanics, Comm. PDE, Vol. 21, 473-506 (1996). | MR | Zbl
[BD] C. Bardos, P. Degond, Global existence for the Vlasov-Poisson Equation in 3 space variables with small initial data, Ann. Inst. H. Poincaré, Anal. Non Lineaire 2, 101–118 (1985). | Numdam | MR | Zbl
[Bo1] F. Bouchut, Existence and Uniqueness of a Global Smooth Solution for the Vlasov-Poisson-Fokker-Planck System in Three Dimensions, J. Funct. Anal., Vol. 111, 239-258 (1993). | MR | Zbl
[Bo2] F. Bouchut, Smoothing effect for the non-linear Vlasov-Poisson-FokkerPlanck System, J. Diff. Eq.,122, 225-238 (1995). | MR | Zbl
[BM] F. Brezzi, P.A. Markowich, The three-dimensional Wigner-Poisson problem : existence, uniqueness and approximation, Math. Meth. Appl. Sci., 14, p. 35-62 (1991). | MR | Zbl
[Ca1] F. Castella, solutions to the Schrodinger-Poisson system, Math. Meth. Mod. Appl. Sci., Vol. 7, N. 8, p. 1051-1083 (1997). 11 | MR | Zbl
[CPe] F. Castella, B. Perthame, Estimations de Strichartz pour les equations de transport cinetique, C. R. Acad. Sci. Paris, t. 322, Ser. I, p. 535-540 (1996). | MR | Zbl
[Ca2] F. Castella, Propagation of space moments in the Vlasov-Poisson equation, a paraître dans Ann. IHP. Anal. Nonlin. (1998). | Numdam | Zbl
[Ca3] F. Castella, Infinite kinetic energy solutions for the Vlasov-Poisson-FokkerPlanck System, a paraître dans Indiana Univ. Math. J. (1998). | MR
[Cz] T. Cazenave, An introduction to nonlinear Schrödinger Equations, Second Edition, Textos de Metodos Matematicas 26, Universidade Federal do Rio de Janeiro (1993).
[CS] J.A. Carillo, J. Soler, On the Vlasov-Poisson-Fokker-Planck equation with measures in Morrey spaces as initial data, | Zbl
[Co] Th. Colin, Smoothing effects for dispersive equations via a generalized Wigner transform, SIAM J. Math. Anal., Vol. 25, No 6, p. 1622-1641 (1994). | MR | Zbl
[DPL1] R.J. Di Perna, P.L. Lions, Solutions globales d’équations du type Vlasov-Poisson, C. R. Acad. Sci. Paris, Vol. 307, 655-658 (1988). | Zbl
[GMMP] P. Gerard, P.A. Markowich, N.J.Mauser, F. Poupaud, Homogenization limits and Wigner transforms, Comm. Pure Appl. Math., Vol. 50, N. 4, p. 323-379 (1997). | MR | Zbl
[GV] J. Ginibre, G. Velo, The global Cauchy problem for some nonlinear Schrödinger equation revisited, Ann. Inst. H. Poincaré, Analyse nonlineaire 2, 309-327 (1985). | Numdam | MR | Zbl
[HH] E. Horst, R. Hunze, Weak solutions of the initial value problem for the unmodified nonlinear Vlasov equation, Math. Meth. Appl. Sci., Vol. 6, 262-279 (1984). | MR | Zbl
[HO] N. Hayashi, T. Ozawa, Smoothing Effect for Some Schrödinger Equations, J. Funct. Anal., 85, p. 307-348, (1989). | MR | Zbl
[Ho1] L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. I, Springer Verlag, New-York-Berlin (1983). | Zbl
[Ho2] L. Hörmander, Hypoelliptic second order differential equations, Acta Math., Vol. 119, 147-171 (1967). 12 | MR | Zbl
[LZ] R. Illner, H. Lange, P. Zweifel, Global existence, uniqueness and asymptotic behaviour of solutions of the Wigner-Poisson and Schrödinger systems, Math. Meth. Appl. Sci., Vol.17, 349-376 (1994). | MR | Zbl
[IN] R. Illner, H. Neunzert, An existence theorem for the unmodified Vlasov equation, Math. Meth. Appl. Sci., Vol. 1, 530-540 (1979). | MR | Zbl
[LPa] P.L. Lions, Th. Paul, Sur les mesures de Wigner, Rev. Mat. Iberoam., Vol. 9, Num. 3, 553-618 (1993). | MR | Zbl
[LPe1] P.L. Lions, B. Perthame, Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system, Invent. Math., Vol. 105, 415-430 (1991). | MR | Zbl
[LPe2] P.L. Lions, B. Perthame, Lemmes de moments, de moyenne et de dispersion, C. R. Acad. Sci. Paris, Vol. 314, 801-806 (1992). | MR | Zbl
[MMP] P.A. Markowich, N. Mauser, F. Poupaud, A Wigner function approach to (semi) classical limits : electrons in a periodic potential, J. Math. Phys., Vol. 35, N. 3, p. 1066-1094 (1994). | MR | Zbl
[Ni] F. Nier, A semi-classical picture of quantum scattering, Ann. Sci. Ec. Norm. Sup., 4. Ser., t. 29, p. 149-183 (1996). | Numdam | MR | Zbl
[Pe] B. Perthame, Time decay, Propagation of Low Moments and Dispersive Effects for Kinetic Equations, Comm. PDE, Vol. 21, 659-686 (1996). | MR | Zbl
[PMi] B. Perthame, S. Mischler, Solutions of the Boltzmann equation with infinite energy, SIAM J. Math. Anal., Vol. 28, N. 5, 1015-1027 (1997). | MR | Zbl
[Pf] K. Pfaffelmoser, Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data, J. Diff. Eq., 95, 281-303 (1992). | MR | Zbl
[Re] G. Rein, growth estimates for the solutions of the Vlasov-Poisson system in the plasma physics case, to appear in Math. Nachrichten. | MR | Zbl
[RW] G. Rein, J. Weckler, Generic global classical solutions of the Vlasov-Fokker-Planck-Poisson system in three dimensions, J. Diff. Eq., Vol. 95, 281-303 (1992). | MR | Zbl
[Sc] J. Schaeffer, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions, Comm. PDE., Vol. 16, N. 8-9, 1313-1335 (1991). | MR | Zbl
[St] R.S. Strichartz, Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J., 44, p. 705-714 (1977). 13 | MR | Zbl
[Ts] Y. Tsutsumi, -Solutions for Nonlinear Schrödinger Equations and Nonlinear Groups, Funk. Ekva., 30, p. 115-125 (1987). | MR | Zbl
[VO] H.D. Victory, B.P. O’Dwyer, On classical solutions of Vlasov-PoissonFokker-Planck systems, Indiana Univ. Math. J., Vol. 39, 105-157 (1990). | Zbl
[Wi] E.P. Wigner, On the quantum correction for thermodynamic equilibrium, Phys. Rev., Vol. 40 (1932). | Zbl
[Ya] K. Yajima, Existence of Solutions for Schrödinger evolution Equations, Commun. Math. Phys., 110, p. 415-426 (1987). | MR | Zbl
[Za] S. Zagatti, The Cauchy problem for Hartree-Fock time dependent equations, Ann. Inst. H. Poincaré, Phys. Th., Vol. 56, N. 4, 357-374 (1992). | Numdam | MR | Zbl