Sur le comportement des solutions d’équations de Schrödinger non linéaires à croissance exponentielle

 Access to full text

 Full (PDF)

1. S. Adachi and K. Tanaka, Trudinger type inequalities in ${ℝ}^N$ and their best exponents, Proceedings in American Mathematical Society, 128 (2000), 2051-2057. Zbl0980.46020MR1646323
2. Adimurthi and O. Druet, Blow-up analysis in dimension 2 and a sharp form of Trudinger-Moser inequality, Communications in Partial Differential Equations, 29 (2004), 295–322. Zbl1076.46022MR2038154
3. H. Bahouri, J.-Y. Chemin and R. Danchin, Fourier Analysis and Nonlinear Partial Differential Equations, Grundlehren der mathematischen Wissenschaften, Springer, (2011). Zbl1227.35004MR2768550
4. H. Bahouri and P. Gérard, High frequency approximation of solutions to critical nonlinear wave equations, American Journal of Math, 121 (1999), 131-175. Zbl0919.35089MR1705001
5. H. Bahouri, M. Majdoub and N. Masmoudi, On the lack of compactness in the 2D critical Sobolev embedding, Journal of Functional Analysis, 260 (2011), 208-252. Zbl1217.46017MR2733577
6. H. Bahouri, M. Majdoub and N. Masmoudi, Lack of compactness in the 2D critical Sobolev embedding, the general case, Journal de Mathématiques Pures et Appliquées, 101 (2014), 415-457. Zbl1305.46024MR3179749
7. H. Bahouri, On the elements involved in the lack of compactness in critical Sobolev embedding, Concentration Analysis and Applications to PDE, Trends in Mathematics, (2013), 1-15. Zbl1291.46030
8. H. Bahouri, S. Ibrahim and G. Perelman, Scattering for the critical 2-D NLS with exponential growth, Journal of Differential and Integral Equations, 27 (2014), 233-268. Zbl1324.35167MR3161603
9. H. Bahouri and G. Perelman, A Fourier approach to the profile decomposition in Orlicz spaces, Mathematical Research Letters, 21 (2014), 33-54. Zbl1311.46030MR3247037
10. H. Bahouri and I. Gallagher, On the stability in weak topology of the set of global solutions to the Navier-Stokes equations, Archive for Rational Mechanics and Analysis, 209 (2013), 569-629. Zbl1283.35061MR3056618
11. H. Bahouri, J.-Y. Chemin and I. Gallagher, Stability by rescaled weak convergence for the Navier-Stokes equations, Notes aux Comptes-Rendus de l’Académie des Sciences de Paris, Ser. I 352 (2014), 305-310. Zbl1294.35056MR3186918
12. H. Bahouri, J.-Y. Chemin and I. Gallagher, Stability by rescaled weak convergence for the Navier-Stokes equations, http://arxiv.org/abs/1310.0256. Zbl1294.35056MR3186918
13. I. Ben Ayed and M. K. Zghal, Characterization of the lack of compactness of $H_{rad}^2\left({ℝ}^4\right)$ into the Orlicz space, Communications in Contemporary Mathematics, 16 (2014), 1-25. MR3231057
14. L. Berlyand, P. Mironescu, V. Rybalko and E. Sandier, Minimax critical points in Ginzburg-Landau problems with semi-stiff boundary conditions : existence and bubbling, Communications in Partial Differential Equations, 39 (2014), 946-1005. Zbl1296.35036MR3196191
15. H. Brézis and J.-M. Coron, Convergence of solutions of H-Systems or how to blow bubbles, Archive for Rational Mechanics and Analysis, 89 (1985), 21-86. Zbl0584.49024MR784102
16. J. Bourgain, A remark on Schrödinger operators, Israel Journal of Mathematics, 77 (1992), 1-16. Zbl0798.35131MR1194782
17. J. Bourgain, Some new estimates on oscillatoryon integrals, Essays on Fourier Analysis in Honor of Elias M. Stein, Princeton Math, 42 (1995), 83-112. Zbl0840.42007MR1315543
18. T. Cazenave, Equations de Schrödinger non linéaires en dimension deux, Proceedings of the Royal Society of Edinburgh. Section A, 84 (1979), 327-346. Zbl0428.35021MR559676
19. J. Colliander, S. Ibrahim, M. Majdoub and N. Masmoudi, Energy critical NLS in two space dimension, Journal of Hyperbolic Differential Equations, 6 (2009), 549-575. Zbl1191.35250MR2568809
20. R. Côte, C. Kenig, A. Lawrie, W. Schlag, Characterization of large energy solutions of the equivariant wave map problem : I http://arxiv.org/abs/1209.3682. Zbl1315.35130
21. R. Côte, C. Kenig, A. Lawrie, W. Schlag, Characterization of large energy solutions of the equivariant wave map problem : II http://arxiv.org/abs/1209.3684. Zbl1315.35131
22. O. Druet, Multibumps analysis in dimension 2 - Quantification of blow up levels, Duke Math. Journal, 132 (2006), 217-269. Zbl1281.35045MR2219258
23. I. Gallagher, G. Koch and F. Planchon, A profile decomposition approach to the $L_t^{\infty }\left(L_x^3\right)$ Navier-Stokes regularity criterion, Mathematische Annalen, 355 (2013), 1527-1559. Zbl1291.35180MR3037023
24. P. Gérard, Description du défaut de compacité de l’injection de Sobolev, ESAIM Contrôle Optimal et Calcul des Variations, 3 (1998), 213-233. Zbl0907.46027
25. P. Gérard, Oscillations and concentration effects in semilinear dispersive wave equations, Journal of Functional Analysis, 133 (1996), 50–68. Zbl0868.35075
26. A. Henrot and M. Pierre, Variations et optimistation de formes, Mathématiques et applications, Springer, 48, (2005). Zbl1098.49001MR2512810
27. S. Ibrahim, M. Majdoub, N. Masmoudi and K. Nakanishi, Scattering for the two dimensional NLS with exponential nonlinearity, Nonlinearity, 25 (2012), 1843-1849. Zbl1241.35188MR2929605
28. S. Ibrahim, M. Majdoub and N. Masmoudi, Double logarithmic inequality with a sharp constant, Proceedings of the American Mathematical Society, 135 (2007), 87–97. Zbl1130.46018MR2280178
29. C. E. Kenig and F. Merle, Global well-posedness, scattering and blow-up for the energy critical focusing non-linear wave equation, Acta Mathematica, 201 (2008), 147-212. Zbl1183.35202MR2461508
30. S. Keraani, On the defect of compactness for the Strichartz estimates of the Schrödinger equation, Journal of Differential equations, 175 (2001), 353-392. Zbl1038.35119MR1855973
31. J. F. Lam, B. Lippman, and F. Tappert, Self trapped laser beams in plasma, Physics of Fluids, 20 (1977), 1176-1179. 
32. P.-L. Lions, The concentration-compactness principle in the calculus of variations. The limit case. I., Revista Matematica Iberoamericana1(1) (1985), 145-201. Zbl0704.49005MR834360
33. P.-L. Lions, The concentration-compactness principle in the calculus of variations. The limit case. II., Revista Matematica Iberoamericana1(2) (1985), 45-121. Zbl0704.49006MR850686
34. G. Mancini, K. Sandeep, and C.Tintarev, Trudinger-Moser inequality in the hyperbolic space ${ℍ}^N$, Advances in Nonlinear Analysis2 (2013), 309-324. Zbl1274.35435MR3089744
35. F. Merle and L. Vega, Compactness at Blow-up Time for L2 Solutions of the Critical Nonlinear Schrödinger Equation in 2D, International Mathematics Research Notices, 8 (1998), 399-425. Zbl0913.35126MR1628235
36. J. Moser, A sharp form of an inequality of N. Trudinger, Indiana University Mathematics Journal, 20 (1971), 1077-1092. Zbl0203.43701MR301504
37. A. Moyua, A. Vargas and L. Vega, Restriction theorems and maximal operators related to oscillatory integrals in ${ℝ}^3$, Duke Mathematical Journal, 96 (1999), 1-28. Zbl0946.42011MR1671214
38. M.-M. Rao and Z.-D. Ren, Applications of Orlicz spaces, Monographs and Textbooks in Pure and Applied Mathematics, 250 (2002), Marcel Dekker Inc. Zbl0997.46027MR1890178
39. B. Ruf and F. Sani, Sharp Adams-type inequalities in ${ℝ}^n$, Transactions of the American Mathematical Society, 2 (2013), 645-670. Zbl1280.46024MR2995369
40. B. Ruf, A sharp Trudinger-Moser type inequality for unbounded domains in ${ℝ}^2$, Journal of Functional Analysis, 219 (2005), 340-367. Zbl1119.46033MR2109256
41. I. Schindler and K. Tintarev, An abstract version of the concentration compactness principle, Revista Mathematica Complutense, 15 (2002), 417-436. Zbl1142.35375MR1951819
42. M. Struwe, A global compactness result for boundary value problems involving limiting nonlinearities, Mathematische Zeitschrift, 187 (1984), 511-517. Zbl0535.35025MR760051
43. N.S. Trudinger, On imbedding into Orlicz spaces and some applications, Journal of Mathematics and Mechanics, 17 (1967), 473-484. Zbl0163.36402MR216286