三维不可压Navier-Stokes方程组模型的整体适定性

Global well-posedness of three-dimensional incompressible Navier-Stokes equations model

研究一个新的三维不可压缩Navier-Stokes方程组模型,新模型与经典的三维不可压缩Navier-Stokes方程组相比较,模型中方程的对流项u·u被调整为(D-12u)·u,其中D=是一个傅里叶乘子,其特征是m(ξ)=ξ.利用能量估计方法和Sobolev空间的相关理论,证明了当任意初值属于L2(3)时,该Navier-Stokes方程组模型的柯西问题是整体适定的.

In this paper,a new three-dimensional incompressible Navier-Stokes equations model is studied.Compared with the classical three-dimensional incompressible Navier-Stokes equations,the convection term u·u of the equations in the new model is adjusted to be(D-12 u)·u,where D=is a Fourier multiplier whose symbol is m(ξ)=ξ.Using the energy estimation method and the related theory of Sobolev space,it is proved that the Cauchy problem of the Navier-Stokes equations is globally well-posed when any initial value belongs to L 2(ℝ3).