On The Energy Equality Of Navier-Stokes Equations Of 2-Dimensions

In this paper,we mainly illustrate the energy conservation problem of distributional solutions of the two-dimensional Navier-Stokes equations.By using dual method,the regularity theory of parabolic equation and function approximation theory,we prove that if the distributional solutions have better integrability:v∈L∞(0,T;L⁽2+ε（（R²））,ε>0,then the energy equality holds:‖v（t）‖22+2∫0t‖▽v（τ）‖22dτ=‖v0‖22.v0∈Lσ2（R2）.The arrangement of this paper is as follows:In the first chapter,we emphasis the physics background and the existed results of energy conservation of Navier-Stokes equations.Meanwhile,we draw a main main conclusion and introduce basic knowledge,inequality and Sign marks in this article.In the second chapter,we study the two-dimensional Navier-Stokes equa-tions linear dual problem.The existence and regularity of solutions to dual equations are proved by the polishing coefficient method and the regularity theory of Stokes system.In the third chapter,now to prove the energy conservation of distributed solution of Navier-Stokes equations is researched.By using the iterative tech-nique of parabolic equation,function approximation theory and the conclusion of the second chapter,we prove that if the distributional solution of the two-dimensional Navier-Stokes equations satisfies v ∈L∞（0,T;L2+ε（R2））,ε>0,then it obeys the energy equality.