The suitable weak solution for the Cauchy problem of the double-diffusive convection system

References

• Hsia CH , Ma T , Wang S . Attractor bifurcation of three-dimensional double-diffusive convection. Z Anal Anwend. 2008;27:233–252.
   Web of Science ®Google Scholar
• Joseph DD . Uniqueness criteria for the conduction-diffusion solution of the Boussinesq equations. Arch Rational Mech Anal. 1969;35:169–177.
   Web of Science ®Google Scholar
• Veronis G . On finite amplitude instability in the thermohaline convection. J Marine Res. 1965;23:1–17.
   Google Scholar
• Jevons WS . On the cirrous form of cloud. London Edinburgh Dublin Philos Mag J Sci Ser. 1857;4(14):22–35.
   Google Scholar
• Stommel H , Arons A , Blanchard D . An oceanographical curiosity: the perpetual salt fountain. Deep-Sea Res. 1956;3:152–153.
   Google Scholar
• Baines PG , Gill A . On thermohaline convection with linear gradients. J Fluid Mech. 1969;37:289–306.
   Web of Science ®Google Scholar
• Brandt A , Fernando HJS . Double-diffusive convection. Washington: American Geophysical Union; 1995.
   Google Scholar
• Huppert HE , Turner JS . Double-diffusive convection. J Fluid Mech. 1981;106:299–329.
   Web of Science ®Google Scholar
• Nield DA , Bejan A . Convection in porous medium. 3rd ed. New York (NY): Springer; 2006.
   Google Scholar
• Radko T , Ball J , Colosi J , Flanagan J . Double-diffusive convection in a stochastic shear. J Phys Oceanography. 2015;45:3155–3167.
   Web of Science ®Google Scholar
• Events Layer-Merging . T. Radko, J.D. Flanagan, S. Stellmach and M.L. Timmermans. Double-diffusive recipes. Part II. J Phys Oceanography. 2014;44:1285–1305.
   Web of Science ®Google Scholar
• Joseph DD . Global stability of the conduction-diffusion solution. Arch Rational Mech Anal. 1970;36:285–292.
   Web of Science ®Google Scholar
• Lions JL , Temam R , Wang SH . On the equations of the large-scale ocean. Nonlinearity. 1992;5:1007–1053.
   Web of Science ®Google Scholar
• Ôtani M , Uchida S . Global sovability of some double-diffusive convection system coupled with Brinkman-Forchheimer equations. Libertas Math. 2013;13:79–107.
   Google Scholar
• Ôtani M , Uchida S . The existence of periodic solutions of some double-diffusive convection system based on Brinkman-Forchheimer equations. Adv Math Sci Appl. 2013;23:77–92.
   Google Scholar
• Ôtani M , Uchida S . Global sovability for double-diffusive convection system based on Brinkman-Forchheimer equation in general domains. Osaka J Math. 2016;53:855–872.
   Web of Science ®Google Scholar
• Piniewski M . Asymptotic dynamics in double-diffusive convection. Appl Math. 2008;35:223–245.
   Google Scholar
• Shir CC , Joseph DD . Convective instability in a temperature and concentration field. Arch Rational Mech Anal. 1968;30:38–80.
   Web of Science ®Google Scholar
• Terasawa K , Ôtani M . Global solvability of double-diffusive convection systems based upon Brinkman-Forchheimer equations. GAKUTO Int Ser Math Sci Appl. 2010;32:505–515.
   Google Scholar
• Chen F , Guo BL , Zeng L . The global well-posedness for the cauchy problem of the double-diffusive convection system. Submitted.
   Google Scholar
• Chen F , Guo BL , Zeng L . The well-posedness of the double-diffusive convection system in a bounded domain. Submitted.
   Google Scholar
• Scheffer V . Hausdorff measure and the Navier-Stokes equations. Commun Math Phys. 1977;55:97–112.
   Web of Science ®Google Scholar
• Caffarelli L , Kohn R , Nirenberg L . Partial regularity of suitable weak solutions of the Navier-Stokes equations. Commu Pure Appl Math. 1982;35:771–831.
   Web of Science ®Google Scholar
• Beirão Da Veiga H . On the suitable weak solutions to the Navier-Stokes equations in the whole space. J Math pures Appl. 1985;64:77–86.
   Web of Science ®Google Scholar
• Guo BL , Yuan GW . On the suitable weak solutions for the cauchy problem of the Boussinesq equations. Nonlinear Anal. 1996;26:1367–1385.
   Web of Science ®Google Scholar
• Boyer F , Fabrie P . Mathematical tools for the study of the incompressible Navier-Stokes equations and related models. New York (NY): Springer Science+Bussiness Media; 2013.
   Google Scholar
• Lions JL , Magenes E . Problémes aux limities non homogénes et applications. vols. I and II. Paris: Dunod; 1969.
   Google Scholar
• Lions JL . Quelques méthodes de resolution de problemes aux limits non-linéairies. Paris: Dunod; 1969.
   Google Scholar