Lorca, Sebastián A.; Boldrini, José Luiz The initial value problem for a generalized Boussinesq model. (English) Zbl 0930.35136 Nonlinear Anal., Theory Methods Appl. 36, No. 4, A, 457-480 (1999). The paper examines the evolution problem for Boussinesq model which describes the coupled mass and heat flow in a viscous incompressible fluid with temperature-dependent viscosity and heat conductivity. Using spectral Galerkin method, the authors prove global existence of weak solutions and local existence of a unique strong solution. Reviewer: O.Titow (Berlin) Cited in 47 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 76R10 Free convection 80A20 Heat and mass transfer, heat flow (MSC2010) Keywords:temperature-dependent heat conductivity; local existence of unique strong solution; viscous incompressible fluid; temperature-dependent viscosity; spectral Galerkin method; global existence of weak solutions PDF BibTeX XML Cite \textit{S. A. Lorca} and \textit{J. L. Boldrini}, Nonlinear Anal., Theory Methods Appl. 36, No. 4, 457--480 (1999; Zbl 0930.35136) Full Text: DOI References: [1] R.A. Adams, Sobolev Spaces, Academic Press, New York, 1975. [2] P.G. Drazin, W.H. Reid, Hydrodynamic Stability, Cambridge University Press, Cambridge, 1981. [3] Hishida, T., Existence and regularizing properties of solutions for the nonstationary convection problem, Funkcialy ekvaciy, 34, 449-474, (1991) · Zbl 0755.35093 [4] J.L. Lions, Quelques Méthodes de Résolution des Problémes aux Limits Non Linéares, Dunod, Paris, 1969. [5] J.L. Lions, E. Magenes, Problèmes aux Limites Non Homogènes et Applications, vol. 1, Dunod, Paris, 1968. [6] S.A. Lorca, J.L. Boldrini, Stationary solutions for generalized Boussinesq models, J. Differential Equations, 124 (2) (1996). · Zbl 0879.35122 [7] S.A. Lorca, J.L. Boldrini, The initial value problem for generalized Boussinesq model: regularity and global existence of strong solutions, Matemática Contemporânea 11 (1996). · Zbl 0861.35080 [8] Morimoto, H., Nonstationary Boussinesq equations, J. fac. sci. univ. Tokyo sect. IA math., 39, 61-75, (1992) · Zbl 0779.76083 [9] K.Óeda, On the initial value problem for the heat convection equation of Boussinesq approximation in a time-dependent domain, Proc. Japan Acad. 64, Ser. A (1988) 143-146. · Zbl 0682.35053 [10] Shinbrot, M.; Kotorynski, W.P., The initial value problem for a viscous heat-conducting fluid, J. math. anal. appl., 45, 1-22, (1974) · Zbl 0283.76026 [11] J. Simon, Compacts sets in the spaceLp(0,T;B), Annali di Matematica Pura ed Applicata, Serie quarta, tomo CXLVI (1987) 65-96. · Zbl 0629.46031 [12] R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam, 1977. [13] H. von Tippelkirch,Über Konvektionszeller insbesondere in flüssigen Schwefel, Beiträge Phys. Atmos. 20 (1956) 37-54. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.