@article{JEDP_1997____A10_0, author = {Klainerman, Sergi\`u and Machedon, Matei}, title = {On the regularity properties of non-linear wave equations}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, year = {1997}, pages = {1-8}, language = {en}, url = {http://dml.mathdoc.fr/item/JEDP_1997____A10_0} }
Klainerman, S.; Machedon, Matei. On the regularity properties of non-linear wave equations. Journées équations aux dérivées partielles, (1997), pp. 1-8. http://gdmltest.u-ga.fr/item/JEDP_1997____A10_0/
[Be] Self-spreading and strength of singularities for solutions to semi-linear wave equations, Annals of Math 118, 1983 no1 187-214. | MR 85c:35057 | Zbl 0522.35064
[B] Fourier transform restriction phenomena for certain lattice subsets and applications to non-linear evolution equations, I, II, Geom. Funct. Analysis 3, (1993), 107-156, 202-262. | MR 95d:35160a | Zbl 0787.35097
[G] A priori estimates and regularity of non-linear waves, Proceedings of ICM, Zurich, 1994.
,[Ke]
, to appear in Comm. in PDE.[K-P-V] The Cauchy problem for the Korteveg-De Vries equation in Sobolev spaces of negative indices, Duke Math Journal 71, no 1, pp 1-21 (1994). | Zbl 0787.35090
, ,[K-M1] Space-time estimates for null forms and the local existence theorem, Comm. Pure Appl. Math, vol XLVI, 1221-1268 (1993). | MR 94h:35137 | Zbl 0803.35095
and[K-M2], On the Maxwell-Klein-Gordon equation with finite energy, Duke Math Journal, vol. 74, no. 1 (1994). | MR 95f:35210 | Zbl 0818.35123
and[K-M3] Finite energy solutions of the Yang-Mills equations in R3+1, Annals of Math. 142, 39-119 (1995). | MR 96i:58167 | Zbl 0827.53056
and[K-M4] Smoothing estimates for null forms and applications, Duke Math Journal, 81, no 1, in celebration of John Nash, 99-133 (1996) Also 1994 IMRN announcement. | MR 97h:35022 | Zbl 0909.35094
and[K-M5] Remark on the Strichartz inequality, International Math Research Notices no 5, 201-220 (1996). | MR 97g:46037 | Zbl 0853.35062
and with appendices by and ,[K-M6] Estimates for null forms and the spaces Hs,δ International Math Research Notices no 17, 853-865 (1996). | MR 98j:46028 | Zbl 0909.35095
and[K-M7] On the regularity properties of a model problem related to wave maps, accepted, Duke Math Journal. | Zbl 0878.35075
and[K-M8] On the optimal local regularity for gauge field theories, accepted, Differential and Integral Equations. | Zbl 0940.35011
and[K-S] Remark on the optimal regularity for equations of Wave Maps type, to appear in Comm PDE. | Zbl 0884.35102
,[K-T] On the local regularity for Yang-Mills equations in R4 + 1, preprint. | Zbl 0924.58010
and ,[L] Counterexamples to local existence for semi-linear wave equations, Amer. J. Math, 118 (1996) no 1 1-16. | MR 97b:35124 | Zbl 0855.35080
[S] Solutions and development of singularities for the SU (2)σ-Model, Comm. Pure Appl. Math, vol XLI 459-469 (1988). | MR 89f:58044 | Zbl 0686.35081
[Sch-So] Local smoothing estimates related to the circular maximal theorem. Math Res. Letters 4 (1997) no 1-15. | MR 98e:42018 | Zbl 0877.42006
,[So] On local existence for non-linear wave equation satisfying variable coefficient null condition, Comm PDE 18 (1993) n0o 11 1795-1821. | MR 94m:35199 | Zbl 0792.35125
[T] The Xsθ spaces and unique continuation for solutions to the semi-linear wave equation, Comm. PDE, 21 (56), 841-887 (1996). | MR 97i:35012 | Zbl 0853.35017
,