Publications [#347987] of Jian-Guo Liu

Papers Published

1. Liu, JG; Pego, RL; Pu, Y, Well-posedness and derivative blow-up for a dispersionless regularized shallow water system, Nonlinearity, vol. 32 no. 11 (October, 2019), pp. 4346-4376 [doi] [high impact paper]
   (last updated on 2024/04/18)

   Abstract:
   We study local-time well-posedness and breakdown for solutions of regularized Saint-Venant equations (regularized classical shallow water equations) recently introduced by Clamond and Dutykh. The system is linearly non-dispersive, and smooth solutions conserve an H 1-equivalent energy. No shock discontinuities can occur, but the system is known to admit weakly singular shock-profile solutions that dissipate energy. We identify a class of small-energy smooth solutions that develop singularities in the first derivatives in finite time.