The Cauchy problem for nonlinear wave equations in the homogeneous Sobolev space

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1. [1] J. Bergh and J. Löfström, Interpolation Spaces, Springer, Berlin, 1976. Zbl0344.46071MR482275
2. [2] P. Brenner, On Lp-Lp' estimates for the wave equation, Math. Z.145 (1975) 251-254. Zbl0321.35052MR387819
3. [3] T. Cazenave and F.B. Weissler, The Cauchy problem for the critical nonlinear Schrödinger equation in HS, Nonlinear Anal. TMA14 (1990) 807-836. Zbl0706.35127MR1055532
4. [4] V. Georgiev and P.P. Schirmer, Global existence of low regularity solutions of non-linear wave equations, Math. Z.219 (1995) 1-19. Zbl0824.35074MR1340845
5. [5] J. Ginibre, Scattering theory in the energy space for a class of nonlinear wave equation, Adv. Stud. Pure Math.23 (1994) 83-103. Zbl0827.35077MR1275396
6. [6] J. Ginibre, T. Ozawa and G. Velo, On the existence of the wave operators for a class of nonlinear Schrödinger equations, Ann. Inst. Henri Poincaré, Physique théorique 60 (1994) 211-239. Zbl0808.35136MR1270296
7. [7] J. Ginibre, A. Soffer and G. Velo, The global Cauchy problem for the critical non-linear wave equation, J. Funct. Anal.110 (1992) 96-130. Zbl0813.35054MR1190421
8. [8] J. Ginibre and G. Velo, The global Cauchy problem for the nonlinear Klein-Gordon equation, Math. Z.189 (1985) 487-505. Zbl0549.35108MR786279
9. [9] J. Ginibre and G. Velo, Regularity of solutions of critical and subcritical nonlinear wave equations, Nonlinear Anal.22 (1) (1994) 1-19. Zbl0831.35108MR1256167
10. [10] J. Ginibre and G. Velo, Generalized Strichartz inequalities for the wave equation, J. Funct. Anal.133 (1995) 50-68. Zbl0849.35064MR1351643
11. [11] L.V. Kapitanski, Weak and yet weaker solutions of semilinear wave equations, Comm. Partial Differential Equations19 (1994) 1629-1676. Zbl0831.35109MR1294474
12. [12] L.V. Kapitanski, Global and unique weak solutions of nonlinear wave equations, Math. Res. Lett.1 (1994) 211-223. Zbl0841.35067MR1266760
13. [13] H. Lindblad, Global solutions of nonlinear wave equations, Comm. Pure Appl. Math.XLV (1992) 1063-1096. Zbl0840.35065MR1177476
14. [14] H. Lindblad, A sharp counterexample to the lacal existence of low-regularity solutions to nonlinear wave equations, Duke Math. J.72 (1993) 503-539. Zbl0797.35123MR1248683
15. [15] H. Lindblad and C.D. Sogge, On existince and scattering with minimal regularity for semilinear wave equations, J. Funct. Anal.130 (1995) 357-426. Zbl0846.35085MR1335386
16. [16] M. Nakamura and T. Ozawa, Low energy scattering for nonlinear Schrödinger equations in fractional order Sobolev spaces, Rev. Math. Phys.9 (3) (1997) 397- 410. Zbl0876.35080MR1446653
17. [17] M. Nakamura and T. Ozawa, The Cauchy problem for nonlinear wave equations in the Sobolev space of critical order, Preprint. Zbl0958.35011
18. [18] H. Pecher, Lp-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichumgen, I, Math. Z.150 (1976) 159-183. Zbl0318.35054MR435604
19. [19] H. Pecher, Nonlinear small data scattering for the wave and Klein-Gordon equation, Math. Z.185 (1984) 261-270. Zbl0538.35063MR731347
20. [20] H. Pecher, Local solutions of semilinear wave equations in Hs+1, Math. Methods Appl. Sci.19 (1996) 145-170. Zbl0845.35069MR1368792
21. [21] R.S. Strichartz, Convolution with kernels having singularities on a sphere, Trans. AMS148 (1970) 461-471. Zbl0199.17502MR256219
22. [22] R.S. Strichartz, A priori estimates for the wave equation and some applications, J. Funct. Anal.5 (1970) 218-235. Zbl0189.40701MR257581
23. [23] R.S. Strichartz, Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J.44 (1977) 705-714. Zbl0372.35001MR512086
24. [24] H. Triebel, Theory of Function Spaces, Birkhäuser, Basel, 1983. Zbl0546.46027

1. Makoto Nakamura, Tohru Ozawa, Small data scattering for nonlinear Schrödinger wave and Klein-Gordon equations