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The lifespan for quasilinear wave equations with multiple propagation speeds in four space dimensions
1. | School of Mathematical Sciences, Fudan University, Shanghai, 200433, China, China |
References:
[1] |
Y. Du and Z. A. Yao, The lifespan for quasi-linear wave equations with multiple-speeds in space dimensions $n\geq3$ , Manuscripta Math., 132 (2010), 343-364.
doi: 10.1007/s00229-010-0350-8. |
[2] |
Y. Du and Y. Zhou, The lifespan for nonlinear wave equations with multiple propagations speeds in 3D , Nonlinear Anal., 68 (2008), 1793-1801.
doi: 10.1016/j.na.2007.01.012. |
[3] |
K. Hidano, An elementary proof of global or almost global existence for quasilinear wave equations , Tohoku Math. J., 56 (2004), 271-287.
doi: 10.2748/tmj/1113246554. |
[4] |
K. Hidano, J. Metcalfe, H. Smith, C. D. Sogge and Y. Zhou, On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles , Trans. Amer. Math. Soc., 362 (2010), 2789-2809.
doi: 10.1090/S0002-9947-09-05053-3. |
[5] |
L. Hörmander, On the fully nonlinear cauchy problem with small data II , in Microlocal Analysis and Nonlinear Waves, IMA Vol. Math. Appl., 30 (eds. Michael Beals, Richard B. Melrose and Jeffrey Rauch), Springer-Verlag, (1991), 51-81.
doi: 10.1007/978-1-4613-9136-4_6. |
[6] |
S. Katayama, Global and almost global existence for systems of nonlinear wave equations with different propagation speeds , Differential Integral Equations, 17 (2004), 1043-1078. |
[7] |
S. Katayama, Global existence for a class of systems of nonlinear wave equations in three dimensions , Chinese Ann. Math. B, 25 (2004), 463-482.
doi: 10.1142/S0252959904000421. |
[8] |
S. Katayama, Global existence for systems of wave equations with nonresonant nonlinearities and null forms , J. Differential Equations, 209 (2005), 140-171.
doi: 10.1016/j.jde.2004.09.012. |
[9] |
S. Klainerman, Uniform decay estimate and the Lorentz invariance of the classical wave equations , Comm. Pure Appl. Math., 38 (1985), 321-332. |
[10] |
S. Klainerman and T. C. Sideris, On almost global existence for nonrelativistic wave equations in 3D , Comm. Pure Appl. Math., 49 (1996), 307-321.
doi: 10.1002/(SICI)1097-0312(199603)49:3<307::AID-CPA4>3.0.CO;2-H. |
[11] |
T. T. Li and Y. M. Chen, Global Classical Solutions for Nonlinear Evolution Equations, Longman Scientific & Technical UK, 1992. |
[12] |
T. T. Li and Y. Zhou, A note on the life-span of classical solutions to nonlinear wave equations in four space dimensions , Indiana Univ. Math. J., 44 (1995), 1207-1248.
doi: 10.1512/iumj.1995.44.2026. |
[13] |
H. Lindblad and C. D. Sogge, Long time existence for small amplitude semilinear wave equation , Amer. J. Math., 118 (1996), 1047-1135.
doi: 10.1353/ajm.1996.0042. |
[14] |
J.Metcalfe and C. D. Sogge, Global existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles , Discrete Contin. Dyn. Syst., 28 (2010), 1589-1601.
doi: 10.3934/dcds.2010.28.1589. |
[15] |
C. X. Miao, J. H. Wu and Z. F. Zhang, Littlewood-Paley Theory and Its Application in Hydrodynamic Equations (Chinese Edition), Monographs on Modern Pure Mathematics 142, Beijing, Science Press, 2012. |
[16] |
T. C. Sideris and S.-Y. Tu, Global existence for systems of nonlinear wave equations in 3D with multiple speeds , SIAM J. Math. Anal., 33 (2001), 477-488.
doi: 10.1137/S0036141000378966. |
[17] |
H. Takamura and K. Wakasa, The sharp upper bound of the lifespan of solutions to critical semilinear wave equations in high dimensions , J. Differential Equations, 251 (2011), 1157-1171.
doi: 10.1016/j.jde.2011.03.024. |
[18] |
C. B. Wang and X. Yu, Recent works on the Strauss conjecture , in Recent Advances in Harmonic Analysis and Partial Differential Equations, Contemp. Math. 581 (eds. Andrea R. Nahmod et al.), Amer. Math. Soc., Providence, RI, (2012), 235-256.
doi: 10.1090/conm/581/11497. |
show all references
References:
[1] |
Y. Du and Z. A. Yao, The lifespan for quasi-linear wave equations with multiple-speeds in space dimensions $n\geq3$ , Manuscripta Math., 132 (2010), 343-364.
doi: 10.1007/s00229-010-0350-8. |
[2] |
Y. Du and Y. Zhou, The lifespan for nonlinear wave equations with multiple propagations speeds in 3D , Nonlinear Anal., 68 (2008), 1793-1801.
doi: 10.1016/j.na.2007.01.012. |
[3] |
K. Hidano, An elementary proof of global or almost global existence for quasilinear wave equations , Tohoku Math. J., 56 (2004), 271-287.
doi: 10.2748/tmj/1113246554. |
[4] |
K. Hidano, J. Metcalfe, H. Smith, C. D. Sogge and Y. Zhou, On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles , Trans. Amer. Math. Soc., 362 (2010), 2789-2809.
doi: 10.1090/S0002-9947-09-05053-3. |
[5] |
L. Hörmander, On the fully nonlinear cauchy problem with small data II , in Microlocal Analysis and Nonlinear Waves, IMA Vol. Math. Appl., 30 (eds. Michael Beals, Richard B. Melrose and Jeffrey Rauch), Springer-Verlag, (1991), 51-81.
doi: 10.1007/978-1-4613-9136-4_6. |
[6] |
S. Katayama, Global and almost global existence for systems of nonlinear wave equations with different propagation speeds , Differential Integral Equations, 17 (2004), 1043-1078. |
[7] |
S. Katayama, Global existence for a class of systems of nonlinear wave equations in three dimensions , Chinese Ann. Math. B, 25 (2004), 463-482.
doi: 10.1142/S0252959904000421. |
[8] |
S. Katayama, Global existence for systems of wave equations with nonresonant nonlinearities and null forms , J. Differential Equations, 209 (2005), 140-171.
doi: 10.1016/j.jde.2004.09.012. |
[9] |
S. Klainerman, Uniform decay estimate and the Lorentz invariance of the classical wave equations , Comm. Pure Appl. Math., 38 (1985), 321-332. |
[10] |
S. Klainerman and T. C. Sideris, On almost global existence for nonrelativistic wave equations in 3D , Comm. Pure Appl. Math., 49 (1996), 307-321.
doi: 10.1002/(SICI)1097-0312(199603)49:3<307::AID-CPA4>3.0.CO;2-H. |
[11] |
T. T. Li and Y. M. Chen, Global Classical Solutions for Nonlinear Evolution Equations, Longman Scientific & Technical UK, 1992. |
[12] |
T. T. Li and Y. Zhou, A note on the life-span of classical solutions to nonlinear wave equations in four space dimensions , Indiana Univ. Math. J., 44 (1995), 1207-1248.
doi: 10.1512/iumj.1995.44.2026. |
[13] |
H. Lindblad and C. D. Sogge, Long time existence for small amplitude semilinear wave equation , Amer. J. Math., 118 (1996), 1047-1135.
doi: 10.1353/ajm.1996.0042. |
[14] |
J.Metcalfe and C. D. Sogge, Global existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles , Discrete Contin. Dyn. Syst., 28 (2010), 1589-1601.
doi: 10.3934/dcds.2010.28.1589. |
[15] |
C. X. Miao, J. H. Wu and Z. F. Zhang, Littlewood-Paley Theory and Its Application in Hydrodynamic Equations (Chinese Edition), Monographs on Modern Pure Mathematics 142, Beijing, Science Press, 2012. |
[16] |
T. C. Sideris and S.-Y. Tu, Global existence for systems of nonlinear wave equations in 3D with multiple speeds , SIAM J. Math. Anal., 33 (2001), 477-488.
doi: 10.1137/S0036141000378966. |
[17] |
H. Takamura and K. Wakasa, The sharp upper bound of the lifespan of solutions to critical semilinear wave equations in high dimensions , J. Differential Equations, 251 (2011), 1157-1171.
doi: 10.1016/j.jde.2011.03.024. |
[18] |
C. B. Wang and X. Yu, Recent works on the Strauss conjecture , in Recent Advances in Harmonic Analysis and Partial Differential Equations, Contemp. Math. 581 (eds. Andrea R. Nahmod et al.), Amer. Math. Soc., Providence, RI, (2012), 235-256.
doi: 10.1090/conm/581/11497. |
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