Global existence, scattering, rigidity and inverse scattering for some quasilinear hyperbolic systems

References

[1] S. Alinhac, The null condition for quasilinear wave equations in two space dimensions I, Invent. Math. 145 (2001), no. 3, 597–618. 10.1007/s002220100165Suche in Google Scholar

[2] R. Bianchini and G. Staffilani, Revisitation of a Tartar’s result on a semilinear hyperbolic system with null condition, preprint (2020), https://arxiv.org/abs/2001.03688. Suche in Google Scholar

[3] D. Christodoulou, Global solutions of nonlinear hyperbolic equations for small initial data, Comm. Pure Appl. Math. 39 (1986), no. 2, 267–282. 10.1002/cpa.3160390205Suche in Google Scholar

[4] A. Hoshiga, The existence of global solutions to systems of quasilinear wave equations with quadratic nonlinearities in 2-dimensional space, Funkcial. Ekvac. 49 (2006), no. 3, 357–384. 10.1619/fesi.49.357Suche in Google Scholar

[5] S. Katayama, Global existence for systems of nonlinear wave equations in two space dimensions. II, Publ. Res. Inst. Math. Sci. 31 (1995), no. 4, 645–665. 10.2977/prims/1195163919Suche in Google Scholar

[6] S. Katayama, Global solutions and the asymptotic behavior for nonlinear wave equations with small initial data, MSJ Mem. 36, Mathematical Society of Japan, Tokyo, 2017. Suche in Google Scholar

[7] S. Klainerman, The null condition and global existence to nonlinear wave equations, Nonlinear Systems of Partial Differential Equations in Applied Mathematics. Part 1 (Santa Fe 1984), Lectures in Appl. Math. 23, American Mathematical Society, Providence (1986), 293–326. Suche in Google Scholar

[8] M. Li, An inverse scattering theorem for ( 1 + 1 ) -dimensional semi-linear wave equations with null conditions, J. Hyperbolic Differ. Equ. 18 (2021), no. 1, 143–167. 10.1142/S021989162150003XSuche in Google Scholar

[9] M. Li, Asymptotic behavior of global solutions to one-dimension quasilinear wave equations, Dyn. Partial Differ. Equ. 18 (2021), no. 2, 81–100. 10.4310/DPDE.2021.v18.n2.a1Suche in Google Scholar

[10] M. Li, Ideal MHD. Part III: Inverse scattering of Alfvén waves in three dimensional ideal magnetohydrodynamics, preprint (2022), https://arxiv.org/abs/2212.02824. 10.1016/j.aim.2023.109363Suche in Google Scholar

[11] M. Li and P. Yu, On the rigidity from infinity for nonlinear Alfvén waves, J. Differential Equations 283 (2021), 163–215. 10.1016/j.jde.2021.02.036Suche in Google Scholar

[12] T. Li and L. Wang, Global Propagation of Regular Nonlinear Hyperbolic Waves, Progr. Nonlinear Differential Equations Appl. 76, Birkhäuser, Boston, 2009. Suche in Google Scholar

[13] H. Lindblad, A remark on global existence for small initial data of the minimal surface equation in Minkowskian space time, Proc. Amer. Math. Soc. 132 (2004), no. 4, 1095–1102. 10.1090/S0002-9939-03-07246-0Suche in Google Scholar

[14] G. K. Luli, S. Yang and P. Yu, On one-dimension semi-linear wave equations with null conditions, Adv. Math. 329 (2018), 174–188. 10.1016/j.aim.2018.02.022Suche in Google Scholar

[15] M. Nakamura, Remarks on a weighted energy estimate and its application to nonlinear wave equations in one space dimension, J. Differential Equations 256 (2014), no. 2, 389–406. 10.1016/j.jde.2013.09.005Suche in Google Scholar

[16] L. Tartar, Some existence theorems for semilinear hyperbolic systems in one space variable, Technical Report 2164, University of Wisconsin, Madison, 1980. Suche in Google Scholar

[17] L. Tartar, From Hyperbolic Systems to Kinetic Theory, Lect. Notes Unione Mat. Ital. 6, Springer, Berlin, 2008. 10.1007/978-3-540-77562-1Suche in Google Scholar

[18] D. Zha, Global and almost global existence for general quasilinear wave equations in two space dimensions, J. Math. Pures Appl. (9) 123 (2019), 270–299. 10.1016/j.matpur.2018.05.009Suche in Google Scholar

[19] D. Zha, On one-dimension quasilinear wave equations with null conditions, Calc. Var. Partial Differential Equations 59 (2020), no. 3, Paper No. 94. 10.1007/s00526-020-01761-1Suche in Google Scholar

[20] D. Zha, W. Peng and Y. Qin, Global existence and asymptotic behavior for some multidimensional quasilinear hyperbolic systems, J. Differential Equations 269 (2020), no. 11, 9297–9309. 10.1016/j.jde.2020.06.051Suche in Google Scholar

[21] D. Zha and M. Sun, Asymptotic behavior of global solutions to some multidimensional quasilinear hyperbolic systems, Dyn. Partial Differ. Equ. 19 (2022), no. 4, 273–284. 10.4310/DPDE.2022.v19.n4.a2Suche in Google Scholar

[22] Y. Zhou, Lifespan of classical solutions to the Cauchy problem of fully nonlinear wave equations with small initial data, Ph.D. thesis, Fudan University, 1992. Suche in Google Scholar

[23] Y. Zhou, Point-wise decay estimate for the global classical solutions to quasilinear hyperbolic systems, Math. Methods Appl. Sci. 32 (2009), no. 13, 1669–1680. 10.1002/mma.1103Suche in Google Scholar