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摘要
In this paper we prove the almost sure existence of global weak solution to the 3D incompressible Navier-Stokes Equation for a set of large data in H-alpha(R-3) or H-alpha(T-3) with 0 < alpha <= 1/2. This is achieved by randomizing the initial data and showing that the energy of the solution modulus the linear part keeps finite for all t >= 0. Moreover, the energy of the solutions is also finite for all t > 0. This improves the recent result of Nahmod, Pavlovic and Staffilani on (SIMA) in which a is restricted to 0 < alpha < 1/4.
- 出版日期2017-9
- 单位复旦大学
