含各向异性非牛顿算子的双扩散对流方程组解的适定性

Well-Posedness of Solutions for the Double-Diffusive Convection System with Anisotropic Non-Newtonian Operators

摘要: 在光滑有界区域$\Omega \subset {ℝ}^3$ 中，考虑一类含各向异性非牛顿算子的双扩散对流方程组的初边值问题。首先用Galerkin方法构建近似解，接着利用能量法建立近似解的一致先验估计，最后借助紧性论证与单调性方法，证明弱解的存在性。

Abstract: We considered the initial-boundary value problem for a class of double-diffusive convection systems involving anisotropic non-Newtonian operators in $\Omega \subset {ℝ}^3$ . We first constructed approximate solutions via the Galerkin method and established uniform a priori estimates by the energy method. Finally, we proved the existence of weak solutions using compactness arguments and the monotonicity method.