摘要
为研究带有分数阶耗散项的三维的Boussinesq方程解的存在性,通过引入光滑子利用正则化方法以及经典的能量方法,证明了三维Boussinesq方程的解是局部存在的,并给出了解的爆破准则.研究结果将之前的二维情形推广到三维情形,并且将带有一般的耗散项结果推广到更复杂的带有分数阶耗散项的Boussinesq方程,这能更精确的反应流体的运动情况.
In order to seek the existence of solution to the 3 D Boussinesq equations with fractional dissipative term, this paper proved that the solution to the 3 D Boussinesq equations exists locally by utilizing the mollifier with the regularizing method and classical energy method, and the blow-up criteria for this solution was given. The results of study extend the previous two dimensional case to three dimensional case, and extend the generalized dissipative terms to more complex Boussinesq equations with fractional dissipative terms, which can more accurately reflect the fluid movement.
出处
《辽宁工程技术大学学报（自然科学版）》
CAS
北大核心
2017年第12期1332-1338,共7页
Journal of Liaoning Technical University (Natural Science)
基金
河北省科技计划项目(16275432)
河北省高等学校科学技术研究项目(Z2017047)
中央高校基本科研业务费专项基金(2016013108)
