带有耗散项的KdV-BO方程解的适定性研究

The well-posedness of KdV-BO equation with dissipation

研究带有一般耗散项的Kd V-BO方程的柯西问题.Kd V-BO方程是描述长波在深槽双流体系统中传播的模型,该流体系统中的低层流体是具有很大密度,交界面处有毛细现象.首先,本文借助半群和压缩映像原理得到了方程柯西问题的局部适定性.其次,基于能量积分估计,对满足一定条件的耗散项,得到方程的整体适定性,最后,文章研究了方程解的指数衰减性.

This paper studies the Cauchy problem of the KdV-BO equation with dissipative term. The equation models are the undirectional propagation of long waves in a two-fluid system, where the lower fluid with greater density is infinitely deep and the interface is subject to capillarity. Firstly, the local well-posedness for the Cauchy problem is obtained by the contraction mamapping theorem. Secondly, based on the energy estimates, the global well-posedness for the equation with the dissipative term which satisfies certain conditions is received. Finally, the exponential decay of the solutions to the equation is proved.