Regularity results for semilinear and geometric wave equations
Shatah, Jalal
Banach Center Publications, Tome 38 (1997), p. 69-90 / Harvested from The Polish Digital Mathematics Library
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     author = {Shatah, Jalal},
     title = {Regularity results for semilinear and geometric wave equations},
     journal = {Banach Center Publications},
     volume = {38},
     year = {1997},
     pages = {69-90},
     zbl = {0895.35065},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv41z1p69bwm}
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Shatah, Jalal. Regularity results for semilinear and geometric wave equations. Banach Center Publications, Tome 38 (1997) pp. 69-90. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv41z1p69bwm/

[000] [1] J. Bergh and J. Löfström, Interpolation Spaces. Grundlehren 223, Springer-Verlag, 1976. | Zbl 0344.46071

[001] [2] P. Brenner and W. von Wahl, Global classical solutions of nonlinear wave equations, Math. Z., 176:87-121, 1981. | Zbl 0457.35059

[002] [3] T. Cazenave, J. Shatah, and A. Tahvildar-Zadeh, Harmonic maps of the hyperbolic space and development of singularities for wave maps and Yang-Mills fields, preprint, 1995. | Zbl 0918.58074

[003] [4] J. Ginibre and G. Velo, The Cauchy problem for the O(N), ℂP(N-1) and Gℂ(N,P) models, Ann. Physics, 142:393-415, 1982. | Zbl 0512.58018

[004] [5] J. Ginibre and G. Velo, The global Cauchy problem for the nonlinear Klein-Gordon equation, Math. Z., 189:487-505, 1985. | Zbl 0549.35108

[005] [6] J. Ginibre and G. Velo, The global Cauchy problem for the nonlinear Klein-Gordon equation revised, Ann. Inst. H. Poincaré, Analyse Non Linéaire, 6:15-35, 1989. | Zbl 0694.35153

[006] [7] M. Grillakis, Regularity and asymptotic behavior of the wave equation with a critical nonlinearity, Ann. of Math., 132:485-509, 1990. | Zbl 0736.35067

[007] [8] M. Grillakis, Classical solutions for the equivariant wave map in 1+2-dimensions, preprint, 1991.

[008] [9] M. Grillakis, A priori estimates and regularity for nonlinear waves, Communication at ICM 94, Zurich, 1994.

[009] [10] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, Math. Lib., volume 18. North-Holland, 1978. | Zbl 0387.46033

[010] [11] K. Jörgens, Das Anfangswertproblem im Grossen für eine Klasse nichtlinearer Wellengleichungen, Math. Zeit., 77:295-308, 1961. | Zbl 0111.09105

[011] [12] L. Kapitanski, Global and unique weak solutions of nonlinear wave equations, Math. Res. Lett., 1:211-223, 1994. | Zbl 0841.35067

[012] [13] S. Klainerman and M. Machedon, Smoothing estimates for null forms and applications, Duke Math. Jour., 81:99-133, 1995. | Zbl 0909.35094

[013] [14] H. Lindblad and C. Sogge, On existence and scattering with minimal regularity for semilinear wave equations, J. Func. Anal., 130:357-426, 1995. | Zbl 0846.35085

[014] [15] B. Marshall, W. Strauss, and S. Wainger, Lp-Lq estimates for the Klein-Gordon equation, J. Math. Pures et Appl., 59:417-440, 1980. | Zbl 0457.47040

[015] [16] H. Pecher, Lp-Abschätzungen und klassische Lösungen für nichtlineare Wellegleichungen, I, Math. Z., 150:151-183, 1976.

[016] [17] G. Ponce and T. Sideris, Local regularity of nonlinear wave equations in threee space dimensions, Comm. Partial Diff. Eq., 18:169-177, 1993. | Zbl 0803.35096

[017] [18] J. Rauch, I. The u5 Klein-Gordon equation. II. Anomalous singularities for semilinear wave equations, in H. Brézis and J. L. Lions, editors, Nonlinear Partial Differential Equations and Their Applications, volume 53, pages 335-364. Pitman, 1981.

[018] [19] I. Segal, Nonlinear Semi Groups, Ann. Math., 78:339-364, 1963. | Zbl 0204.16004

[019] [20] J. Shatah and M. Struwe, Regularity results for nonlinear wave equations, Ann. Math., 138:503-518, 1993. | Zbl 0836.35096

[020] [21] J. Shatah and M. Struwe, Well-posedness in the energy space for semilinear wave equations with critical growth, IMRN, 7:303-309, 1994. | Zbl 0830.35086

[021] [22] J. Shatah and A. Tahvildar-Zadeh, Regularity of harmonic maps from the Minkowski space into rotationally symmetric manifolds, Comm. Pure Appl. Math., XLV:947-971, 1992. | Zbl 0769.58015

[022] [23] J. Shatah and A. Tahvildar-Zadeh, On the Cauchy problem for equivariant wave maps, Comm. Pure Appl. Math, 47:719-754, 1994. | Zbl 0811.58059

[023] [24] W. Strauss, Nonlinear invariant wave equations, in G. Velo and A. S. Wightman, editors, Invariant Wave Equations, pages 197-249. Springer-Verlag, Berlin, 1978.

[024] [25] W. Strauss, Nonlinear Scattering Theory at Low Energy, J. Funct. Anal., 41:110-133, 1981. | Zbl 0466.47006

[025] [26] R. S. Strichartz, Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J., 44:705-714, 1977. | Zbl 0372.35001

[026] [27] M. Struwe, Globally regular solutions to the u5 Klein-Gordon equation, Annali Sc. Norm. Sup. Pisa (Ser. 4), 15:495-513, 1988.

[027] [28] M. Struwe, Geometric Evolution Problems, Park City Geom. Ser. of the Amer. Math. Soc., Providence, R.I., 1992.