Wei, Long Wave breaking, global existence and persistent decay for the Gurevich-Zybin system. (English) Zbl 1448.35505 J. Math. Fluid Mech. 22, No. 4, Paper No. 47, 14 p. (2020). Summary: In this paper, the blow-up phenomenon, global existence and persistent decay of the solutions to the Gurevich-Zybin system are studied. We show that the system possesses a so called critical threshold phenomena, that is, global smoothness versus finite time breakdown depends on whether the initial configuration crosses an intrinsic critical threshold. We prove that a finite maximal life span for a solution necessarily implies wave breaking for this solution, and show some conditions which are local-in-space on the initial data to ensure wave-breaking for this system by making use of the characteristics method, otherwise, the system has a global smooth solution. Furthermore, we establish the persistence properties for the system in weighted \(L^p\) spaces. Cited in 2 Documents MSC: 35Q75 PDEs in connection with relativity and gravitational theory 35Q86 PDEs in connection with geophysics 35Q31 Euler equations 35Q60 PDEs in connection with optics and electromagnetic theory 35L60 First-order nonlinear hyperbolic equations 35B44 Blow-up in context of PDEs 83C35 Gravitational waves 86A05 Hydrology, hydrography, oceanography Keywords:Gurevich-Zybin system; global well-posedness; blow-up; wave breaking; persistence PDFBibTeX XMLCite \textit{L. Wei}, J. Math. Fluid Mech. 22, No. 4, Paper No. 47, 14 p. (2020; Zbl 1448.35505) Full Text: DOI References: [1] Aldroubi, A.; Gröchenig, K., Nonuniform sampling and reconstruction in shift-invariant spaces, SIAM Rev., 43, 585-620 (2001) · Zbl 0995.42022 · doi:10.1137/S0036144501386986 [2] Brandolese, L., Breakdown for the Camassa-Holm equation using decay criteria and persistence in weighted spaces, Int. Math. Res. 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