Etude mathématique de modèles asymptotiques pour les ondes d'Alfven
Thèses d'Orsay, no. 610 (2001) , 122 p. 
@phdthesis{BJHTUP11_2001__0610__P0_0,
     author = {Serra De Oliveira, Filipe},
     title = {Etude math\'ematique de mod\`eles asymptotiques pour les ondes {d'Alfven}},
     series = {Th\`eses d'Orsay},
     publisher = {Universit\'e de Paris-Sud U.F.R. Scientifique d'Orsay},
     number = {610},
     year = {2001},
     language = {fr},
     url = {http://www.numdam.org/item/BJHTUP11_2001__0610__P0_0/}
}
TY  - BOOK
AU  - Serra De Oliveira, Filipe
TI  - Etude mathématique de modèles asymptotiques pour les ondes d'Alfven
T3  - Thèses d'Orsay
PY  - 2001
IS  - 610
PB  - Université de Paris-Sud U.F.R. Scientifique d'Orsay
UR  - http://www.numdam.org/item/BJHTUP11_2001__0610__P0_0/
LA  - fr
ID  - BJHTUP11_2001__0610__P0_0
ER  - 
%0 Book
%A Serra De Oliveira, Filipe
%T Etude mathématique de modèles asymptotiques pour les ondes d'Alfven
%S Thèses d'Orsay
%D 2001
%N 610
%I Université de Paris-Sud U.F.R. Scientifique d'Orsay
%U http://www.numdam.org/item/BJHTUP11_2001__0610__P0_0/
%G fr
%F BJHTUP11_2001__0610__P0_0
Serra De Oliveira, Filipe. Etude mathématique de modèles asymptotiques pour les ondes d'Alfven. Thèses d'Orsay, no. 610 (2001), 122 p. http://numdam.org/item/BJHTUP11_2001__0610__P0_0/

[1] D. Bekiranov, T. Ogawa and G. Ponce : On the well-posedness of Benney's interaction equation for short and long waves, Adv. in Diff. Eq., Vol. 6, 919-937 (1996). | MR | Zbl

[2] M. Ben-Hartzi and J-C. Saut : Uniform decay estimates for a class of oscillatory integrals and applications, Diff. Int. Eq., vol. 12, 137-145 (1999). | MR | Zbl

[3] H. Berestycki and P-L. Lions :Nonlinear scalar fields I-existence of a ground state, Archs ration. Mech. Analysis, Vol. 32, 313-345 (1983). | MR | Zbl | DOI

[4] G. Boling and M. Changxing : Well-posedness of Cauchy problem for coupled system of long-short wave equations, J. Partial Diff. Eqs, vol. 11, 83-96, (1998). | MR | Zbl

[5] J. Bona : On the stability theory of solitary waves, Proc. R. Soc. Lond., Vol. A344, 363-374 (1975). | MR | Zbl

[6] A. De Bouard : Analytic solutions to nonelliptic nonlinear Schrödinger equations, J. Diff. Eq., vol. 104, 196-213 (1993). | MR | Zbl | DOI

[7] T. Cazenave and A. Haraux : Introduction aux problèmes d'évolution semi-linéaires, Mathématiques et Applications, Soc. Math. Appl. et Ind., Palaiseau (1990). | MR | Zbl

[8] S. Champeaux, T. Passot and P-L. Sulem. : Alfvén wave filamentation, J.Plasma Phys., vol. 58, 665-690 (1997). | DOI

[9] S. Champeaux, D. Laveder, T. Passot and P-L. Sulem : Remarks on the parallel propagation of small-amplitude dispersive Alfven waves, Nonlinear Processes in Geophysics, Vol.6, 169-178 (1999). | DOI

[10] F. Christ and M. Weinstein : Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation, J. Funct. Analysis, vol. 100, 87-109 (1991). | MR | Zbl | DOI

[11] X. Feng and F. Wei : on global solutions to a nonlinear Alfvén wave equation, Ann. Pol. Math., vol. 62, 155-172 (1995). | MR | Zbl | DOI

[12] J. Francia, F. Ruiz and J. Torrea : Caldéron-Zygmund theory for Operator-Valued Kernels, Advances in Math., vol.62, 7-48 (1986). | MR | Zbl

[13] J. Frutos and J.M. Sanz-Serna : Accuracy and conservation properties in numerical integration : The case of the KdV equation, J. Numer. Math, vol.75, 421-445 (1997). | MR | Zbl | DOI

[14] T. Gallay and G. Schneider : KP description of unidirectional long waves-The model case, Preprint, Prépublications d'Orsay (1999). | MR | Zbl

[15] C.S. Gardner and G.K. Morikawa : Report NYO-9082, Courant Institute of Math. Sci., New York University (1960).

[16] A. Gazol, T. Passot and P-L. Sulem : Nonlinear dynamics of obliquely propagating Alfvén waves, J. Plasma Phys., vol.60, 95-109 (1998). | DOI

[17] R. T. Glassey : Approximate Solutions for the Zakharov Equations via Finite Differences, J. Comp. Phys., vol 100, 377-383 (1992). | MR | Zbl | DOI

[18] H. Grad : The guiding center plasma, Proc. Sympos. Appl. Maths., AMS-Providence, Vol. 18, 162-248 (1967). | MR | DOI

[19] A. Hasegawa, Optical Solitons in fibers, Springer-Verlag (1989).

[20] N. Hayashi : Global existence of small analytic solutions to nonlinear Schrödinger equations, Duke Math. J., vol 60, 717-727 (1990). | MR | Zbl | DOI

[21] N. Hayashi and S. Saitoh : Analyticity and global existence of small solutions to some nonlinear Schrödinger equations, Comm.Math.Phys., vol.129, 27-41 (1990). | MR | Zbl

[22] N. Hayashi : The initial value problem for the derivative nonlinear Schrödinger equation, Non-linear Anal. TMA, vol 20, 823-833 (1993). | MR | Zbl

[23] E.H. Holt and R.E. Haskell : Foundations of plasma dynamics, The Macmillan Company, New York.

[24] R. Iorio Jr. and W. Nunes : On equations of KP-type, Proc. Royal Soc. Ed., vol. 128A, 725-743 (1998). | MR | Zbl | DOI

[25] B. B. Kadomtsev, V.I. Petviashvili : On the stability of solitary waves in weakly dispersive media, Soviet. Phys. Dokl. vol. 15, 539-541 (1967). | Zbl

[26] T. Kato and G. Ponce : Commutator estimates for and the Euler and Navier-Stockes equations, Comm. Pure Appl. Math., vol. 41, 891-907 (1988). | MR | Zbl

[27] D. Kaup and A. Newell : An exact solution for a derivative nonlinear Schrödinger equation, J. Math. Phys., vol.19, 798-801 (1978). | MR | Zbl | DOI

[28] C. Kenig, G. Ponce and L. Vega : Oscillatory integrals and regularity of dispersive equations, Ind. Uni. Math. J., vol.40, 33-68 (1991). | MR | Zbl | DOI

[29] C. Kenig, G. Ponce and L. Vega : On the generalized Benjamin-Ono equation, Trans. Amer. Math. J., vol. 342, 155-172 (1994). | MR | Zbl | DOI

[30] C. Kenig, G. Ponce and L. Vega : Small solutions to nonlinear Schrödinger equations, Ann. Inst. Henri Poincaré, vol. 110, 255-288 (1993). | MR | Zbl | Numdam | DOI

[31] C.F. Kennel, B. Buti, T. Hada and R. Pellat : Non linear, dispersive, elliptically polarized Alfvïn waves, J. Phys. Fluids, vol.31, 1949-1958 (1988). | MR | Zbl | DOI

[32] P. Kirmann, G. Schneider and A. Mielke, The validity of modulation equations for extended systems with cubic nonlinearities, Proc. Royal Society Edinburgh, vol. 122A, pp-85 (1992). | MR | Zbl | DOI

[33] D. Laveder, T. Passot, P. L. Sulem, Physica D, 152-153, 694 (2001). | Zbl

[34] P. Laurençot : On a nonlinear Schrödinger equation arising in the theory of water waves, Nonlinear Analysis T.M.A, Vol.4, 509-527 (1995). | MR | Zbl

[35] J.H. Lee : Global solvability of the derivative nonlinear Schrödinger equation, Trans. Amer. Math. Soc., vol 314, 107-118 (1989). | MR | Zbl

[36] E. Mjolhus and J. Wyller : Nonlinear Alfvén waves in a finite-beta plasma, J. Plasma Physics, vol.40, 299-318 (1988). | DOI

[37] J-L. Lions and E. Magenes : Problèmes aux limites non homogènes et applications, Paris, Dunod (1968). | Zbl

[38] C. Longmire : Elementary Plasma Physics, Interscience Publ, (1963). | Zbl

[39] E. Mjolhus and T. Hada : Oblique stability of circulary polarized MHD waves, J. Plasma Physics, vol.43, 257-268 (1990). | DOI

[40] E. Mjolhus: Report 48, Dept App. Math., University of Bergen (1974).

[41] E. Mjollhus and T. Hada, Nonlinear Waves in Space Plasmas, Terrapub, Tokyo (1997).

[42] E. Mjolhus and T. Hada : Oblique stability of circularly polarized MHD waves, J. Plasma Physics, vol. 43, pp-257 (1990). | DOI

[43] E. Mjolhus and S. Wyller, Physica Scripta, vol. 33, p-442 (1986). | DOI

[44] E. Mjolhus and S. Wyller, Nonlinear Alfvén waves in a finite beta-plasma, J. Plasma Physics, vol. 40, pp-299 (1988). | DOI

[45] G. K. Morikawa, Non linear diffusion of flood waves in rivers, Comm. Pure Appl. Maths, vol. 10, 291-303 (1957). | MR | Zbl

[46] T. Ozawa : On the nonlinear Schrödinger equations of derivative type, Indiana U. Math. J., vol 45, 137-163 (1996). | MR | Zbl | DOI

[47] T. Ozawa and Y. Tsutsumi : Existence and Smoothing Effect of Solutions for the Zakharov Equations, Publ. RIMS. Kyoto Univ., Vol.28, 329-361 (1992). | MR | Zbl

[48] G. Ponce and J-C. Saut : Well-posedness for the Benney-Zakharov-Rubenchick system, Preprint (2000). | MR

[49] M.S. Ruderman : Non linear internal waves in a flood of infinite depht in the presence of a horizontal magnetic field, Fluid dyn., vol.22, 299-305 (1987). | Zbl

[50] J.M. Sanz-Serna and J.G. Verwer : Conservative and non-conservative scheme for the solutions of the nonlinear Schrödinger equations, IMA J. Math. Anal., vol.6, 25-42 (1986). | MR | Zbl

[51] G. Schneider : Approximation of the Korteweg-de Vries Equation by the Nonlinear Schrödinger Equation, J. Diff. Equations, vol.147, pp-333 (1988). | MR | Zbl | DOI

[52] Y. Shibata and Y. Tsutsumi, Local existence of solutions for the initial boundary problem of fully nonlinear wave equation, Nonlinear Analysis TMA, Vol.11, 335-365 (1987). | MR | Zbl

[53] H. Takaoka, Well-posedness for the one dimensional nonlinear Schrödinger Equation with the derivative nonlinearity, (1998). | MR | Zbl

[54] M.E. Taylor : Pseudo-differential operators and nonlinear PDE, Lecture Notes in Mathematics, vol. 416, Springer-Berlin (1974). | MR | Zbl

[55] L. Vega : Doctoral Thesis, Univ. Autonoma de Madrid, Spain (1987).

[56] M. Tsutsumi and S. Hatano : Well-posedness of the Cauchy Problem for Benney's first equations of Long Wave Short Wave interactions, Funkcialaj Ekvacioj, Vol.37, 289-316 (1994). | MR | Zbl

[57] M. Tsutsumi and S. Hatano : Well-posedness of the Cauchy Problem for the Long Wave Short Wave resonance equations, Nonlinear Analysis T.M.A, Vol.22, 155-171 (1994). | MR | Zbl

[58]M. Weinstein : Modulational stability of ground states of nonlinear Schrödinger equations, SIAM J. Math. Anal., Vol.16, 472-491. | MR | Zbl | DOI

[59] M. Weinstein : Lyapunov stability of ground states of Nonlinear dispersive evolution equations, Comm. Pure and Apl. Math., Vol.39, 51-68 (1986). | MR | Zbl

[60] J. Wyller, T. Fla and E. Mjolhus : The effect of resonant particles on Alfvén solitons, Physica D, vol.39, 405-422 (1989). | MR | Zbl | DOI

[61] V. Zakharov, Collapse of Langmuir Waves, Sov. Phys. JETP, Vol.35, 908-914 (1972).

[62] V.E. Zakharov and A.M. Rubenchik : Nonlinear interaction between high and low frequency waves, Prikl. Mat. Techn. Fiz., Vol.5, 84-98 (1972).