[1] Bahouri H, Chemin J-Y, Danchin R. Fourier Analysis and Nonlinear Partial Differential Equations. Berlin, Heidelberg:Springer, 2011 [2] Bresch D, Desjardins B. Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model. Commun Math Phy, 2003, 238:211-223 [3] Chen Q, Miao C, Zhang Z. On the well-posedness for the viscous shallow water equations. SIAM J Math Anal, 2008, 40(2):443-474 [4] Choboter P F, Swaters G E. Modeling equator-crossing currents on the ocean bottom. Canadian Applied Mathematics Quarterly, 2000, 8(4):367-385 [5] Cheng F, Xu C. Analytical smoothing effect of solutions for the Boussinesq equations. Acta Math Sci, 2019, 39B(1):165-179 [6] Danchin R. Global existence in critical spaces for compressible Navier-Stokes equations. Invent Math, 2000, 141(3):579-614 [7] Danchin R. Global existence in critical spaces for flows of compressible viscous and heat-conductive gases. Arch Rational Mech Anal, 2001, 160:1-39 [8] Danchin R. Fourier analysis methods for PDEs. Lecture Notes, 2005 [9] Dellar P J, Salmon R. Shallow water equations with a complete Coriolis force and topography. Phy Fluids, 2005, 17(10):1-100 [10] Ferrari S, Saleri F. A new two dimensional shallow-water model including pressure effects and slow varying bottom topography. Math Model Numer Anal, 2004, 38(2):211-234 [11] Guo Z, Jiu Q, Xin Z. Spherically symmetric isentropic compressible flows with density-dependent viscosity coefficients. SIAM J Math Anal, 2008, 39(5):1402-1427 [12] Hao C, Hsiao L, Li H. Cauchy problem for viscous rotating shallow water equations. J Differ Equ, 2013, 247(12):3234-3257 [13] Haspot B. Cauchy problem for viscous shallow water equations with a term of capillarity. Math Models Methods Appl Sci, 2010, 20:1049-1087 [14] Li H, Li J, Xin Z. Vanishing of vacuum states and blow-up phenomena of the compressible Navier-Stokes equations. Commun Math Phy, 2008, 281:401-444 [15] Muñoz-Ruiz M L. On a non-homogeneous bi-layer shallow water problem:smoothness and uniqueness results. Nonlinear Anal, 2004, 59(3):253-282 [16] Narbona-Reina G, Zabsonré J D, Fernández-Nieto E D, Bresch D. Derivation of a bilayer model for shallow water equations with viscosity. Cmes Comput Model Engin Ences, 2009, 43(1):27-71 [17] Qin H, Xie C, Fang S. Remarks on regularity criteria for 3D generalized MHD equations and Boussinesq equations. Acta Math Sci, 2019, 39A(2):316-328 [18] Roamba B, Zabsonre J D. A bidimensional bi-layer shallow-water model. Elec J Differ Equ, 2017, 168:1-19 [19] Vallis G K. Atmospheric and Oceanic Fluid Dynamics:Fundamentals and Large-Scale Circulation. Cambridge:Cambridge University Press, 1996 [20] Wang W, Xu C. The cauchy problem for viscous shallow water equations. Revista Matematica Iberoamericana, 2005, 21(1):1-24 [21] Zabsonré J D, Narbona-Reina G. Existence of a global weak solution for a 2D viscous bi-layer Shallow Water model. Nonlinear Analysis:Real World Applications, 2009, 10(5):2971-2984 |