The rescaling method for some critical quasilinear wave equations with the divergence form of the nonlinearity

References

• Glassey RT . Finite-time blow-up for solutions of nonlinear wave equations. Math Z. 1981;177:323–340.
   Web of Science ®Google Scholar
• Glassey RT . Existence in the large for □u = F(u) in two space dimensions. Math Z. 1981;178:233–261.
   Web of Science ®Google Scholar
• Lindblad H . Blow up for solutions of □u = |u|p with small initial data. Commun Par Differ Equ. 1990;15(6):757–821.
   Web of Science ®Google Scholar
• Schaeffer J . The equation □u = |u|p for the critical value of p . Proc Roy Soc Edinburgh. 1985;101:31–44.
   Google Scholar
• Zhou Y . Blow up of classical solutions to □u = |u|1+α in three space dimensions. J Par Differ Equ. 1992;5:21–32.
   Google Scholar
• Strauss WA . Nonlinear wave equations. Vol. 73, CBMS regional conference series in mathematics. Providence (RI): AMS; 1989.
   Google Scholar
• Yordanov B , Zhang QS . Finite time blow up for critical wave equations in high dimensions. J Funct Anal. 2006;231:361–374.
   Web of Science ®Google Scholar
• Takamura H , Wakasa K . The sharp upper bound of the lifespan of solutions to critical semilinear wave equations in high dimensions. J Differ Equ. 2011;251:1157–1171.
   Web of Science ®Google Scholar
• Strauss WA . Nonlinear scattering theory at low energy. J Funct Anal. 1981;41:110–133.
   Web of Science ®Google Scholar
• Wang C , Yu X . Recent works on the Strauss conjecture. In: Nahmod Andrea R , Sogge Christopher D , Zhang Xiaoyi , Shijun Zheng , editors. Recent advances in harmonic analysis and partial differential equations. Vol. 581, Contemporary mathematics. Providence (RI): American Mathematical Society; 2012. p. 235–256.
   Google Scholar
• John F . Blow-up of solutions of nonlinear wave equations in three space dimensions. Manuscr Math. 1979;28:235–268.
   Web of Science ®Google Scholar
• Kato T . Blow-up of solutions of some nonlinear hyperbolic equations. Commun Pure Appl Math. 1980;33:501–505.
   Web of Science ®Google Scholar
• Li T , Zhou Y . A note on the life-span of classical solutions to nonlinear wave equations in four space dimensions. Indiana Univ Math J. 1995;44:1207–1248.
   Web of Science ®Google Scholar
• Rammaha MA . Nonlinear wave equations in high dimensions. In: Proceeding of the International Conference on Theory and Applications of Differential Equations (Columbus, OH, March 21--25, 1988). Vol. I, II ; Athens (OH): Ohio University Press; 1989. p. 322–326.
   Google Scholar
• Sideris TC . Nonexistence of global solutions to semilinear wave equations in high dimensions. J Differ Equ. 1984;52:378–406.
   Web of Science ®Google Scholar
• Tataru D . Strichartz estimates in the hyperbolic space and global existence for the semilinear wave equation. Trans Amer Math Soc. 2001;353:795–807.
   Web of Science ®Google Scholar
• Yordanov B , Zhang QS . Finite time blowup for wave equations with a potential. SIAM J Math Anal. 2005;36:1426–1433.
   Web of Science ®Google Scholar
• Zhou Y , Han W . Life-span of solutions to critical semilinear wave equations. Commun Par Differ Equ. 2014;39:439–451.
   Web of Science ®Google Scholar
• Hormander L . On the fully nonlinear Cauchy problem with small data. II. Microlocal analysis and nonlinear waves, Minneapolis, MN, 1988–1989. Vol. 30, IMA volumes in mathematics and its applications. New York (NY): Springer; 1991. p. 51–81.
   Google Scholar
• Li T , Xin Y . Life-span of classical solutions to fully nonlinear wave equations. Commun Par Differ Equ. 1991;16:909–940.
   Web of Science ®Google Scholar
• Han W . Life-span of classical solutions to one dimensional initial-boundary value problems for general quasilinear wave equations. J Math Anal Appl. 2012;387:291–309.
   Web of Science ®Google Scholar
• Han W , Zhou Y . Blow up for some semilinear wave equations in multi-space dimensions. Commun Par Differ Equ. 2014;39:651–665.
   Web of Science ®Google Scholar
• Han W . Life-span of classical solutions to one dimensional initial-boundary value problems for general quasilinear wave equations with Robin boundary conditions. J Math Anal Appl. 2013;397:46–74.
   Web of Science ®Google Scholar
• Li T , Chen YM . Global classical solutions for nonlinear evolution equations. Vol. 45, Pitman monographs and surveys in pure and applied mathematics. Essex, England: Longman Scientific & Technical; 1992.
   Google Scholar
• Li T , Chen YM . Initial value problems for nonlinear wave equations. Commun Partial Differ Equ. 1988;13:383–422.
   Web of Science ®Google Scholar