Blow Up Criterion For The 2D Dispersive Navier-Stokes System

In the whole space or bounded region,this dissertation establishes the blow up criterion of the local strong solution in two-dimensional dissipative Navier-Stokes system.that is,in the whole space,under the condition of(?)?(T*is the maximum time of the solution),the local strong solution of the system will not be blasting;in the bounded region,under the condition of(?)is any small positive number),the local strong solution of the system will not be blasting.It consists of three chapters.In the first chapter,for the system,We introduce the background and contents of the study in brief,and carry out the corresponding deformation.In the second chapter,in the whole space,for the local strong solution of the dissipative Navier-Stokes system,We use the principle of the regularity of solution to prove the nonsingularity of strong solution under the condition of(?),that is the theorem 2.3.In the third chapter,in the bounded region,for the local strong solution of the dissipative Navier-Stokes system,We use the principle of internal regularity and near regularity to prove the nonsingularity of strong solution under the condition of(?)<?(p=2+?,? is any small positive number),that is the theorem 3.6.