一类广义Boussinesq方程组解的存在性及正则性

Existence and regularity criterion for a class of generalized Boussinesq equations

为研究带有分数阶耗散项的Boussinesq方程组的解存在性、唯一性以及解的相关定性性质,利用经典的Galerkin方法和能量方法研究了带有分数阶耗散项的广义Boussinesq方程组弱解的存在性及其解的正则性问题,获得了方程弱解的局部存在性结果,借助Gagliardo-Nirenberg不等式及其它不等式给出了解的正则性准则,这些结果推广和延伸了先前的相关结果,揭示了流体运动的物理现象,并对流体水力学的发展提供了必要的理论依据.

In order to survey the existence and uniqueness of solution as well as the relevant quahtatlve properties for Boussinesq equations with fractional dissipative term, classical Galerkin method and energy method were used to obtain the weak solution and regularized solution for the generalized Boussinesq equations, and the weak solution is local. The regularized results was studied with the aid of Gagliardo-Nirenberg inequality and the others inequality. The results of study improve and extend the ones in the previous works to a large extent, reveal the physical phenomenon of fluid motion, and provide the necessary theoretical basis for the development of fluid hydraulics.