Regularity results for nonlinear wave equations
作者： Jalal Shatah , Michael Struwe
DOI: 10.2307/2946554
关键词:
摘要: … with a smooth function (; that is, a semilinear wave equation of type (0.1) in 1R4 x IR. Note that c = (2g"'(0))/3 may have the "wrong" sign. The norm of w can be estimated in terms of the …
princeton.edu
jstor.org
sci-hub.se 参考文章(12)
Konrad J�rgens, Das Anfangswertproblem in Großen für eine Klasse nichtlinearer Wellengleichungen Mathematische Zeitschrift. ,vol. 77, pp. 295- 308 ,(1961) , 10.1007/BF01180181
Hans Triebel, Interpolation Theory, Function Spaces, Differential Operators ,(1978)
C. E. Kenig, A. Ruiz, C. D. Sogge, Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators Duke Mathematical Journal. ,vol. 55, pp. 329- 347 ,(1987) , 10.1215/S0012-7094-87-05518-9
Robert S. Strichartz, Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations Duke Mathematical Journal. ,vol. 44, pp. 705- 714 ,(1977) , 10.1215/S0012-7094-77-04430-1
J. Shath, A. Tahvildar-Zadeh, Regularity of harmonic maps from the Minkowski space into rotationally symmetric manifolds Communications on Pure and Applied Mathematics. ,vol. 45, pp. 947- 971 ,(1992) , 10.1002/CPA.3160450803
Robert S. Strichartz, Convolutions with kernels having singularities on a sphere Transactions of the American Mathematical Society. ,vol. 148, pp. 461- 471 ,(1970) , 10.1090/S0002-9947-1970-0256219-1
Manoussos G. Grillakis, Regularity and asymptotic behavior of the wave equation with a critical nonlinearity Annals of Mathematics. ,vol. 132, pp. 485- 509 ,(1990) , 10.2307/1971427
Manoussos G. Grillakis, Regularity for the wave equation with a critical nonlinearity Communications on Pure and Applied Mathematics. ,vol. 45, pp. 749- 774 ,(1992) , 10.1002/CPA.3160450604
Time decay for the nonlinear Klein-Gordon equation Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 306, pp. 291- 296 ,(1968) , 10.1098/RSPA.1968.0151
J. Ginibre, G. Velo, The Global Cauchy Problem for the Non Linear Klein-Gordon Equation. Mathematische Zeitschrift. ,vol. 189, pp. 487- 505 ,(1985) , 10.1007/BF01168155