Blow Up Criterion For 3d Dispersive Navier-Stokes System On Bounded Domain

In this paper,we establish a blow up criterion for strong solutions to the 3D dispersive Navier-Stokes system on bounded domain.This paper consists of three chapters.In chapter one,firstly,we briefly introduce the mathematical formulation of the dispersive Navier-Stokes system and the meaning of the related symbols.Then,we state the development experience and the research status of the system.lastly,we show the main purpose of this paper base on existing research results,and give The conclusion of this paper as follows:Theorem 1.1(Blow up criterion)Let n = 3 and(?,u)be the local strong solutions of the dispersive Navier-Stokes system on bounded domain.If the so-lution blows up in the finite time(i.e.the lifespan of the solution T*<+?),thenIn chapter two,we provide some known conclusions that will play a crucial role in the proof of theorem 1.1.In chapter three,The proof of theorem 1.1.Before giving the proof of theorem 1.1,by introducing the new variable,we can reformulate theorem 1.1 into the equivalent proposition.By proving the equivalent proposition to complete the proof of theorem 1.1.In the proof,we mainly use the energy method to estimate the regularity of the local strong solution.however,it is difficult to estimate higher order item of the local strong solution.But,by means of the difference method and locally flatting technology,we overcame the difficulty,then complete the proof.