In this paper, we shall prove that the Koch-Tataru solution u to the incompressible Navier-Stokes equations in Rd satisfies the decay estimates involving some borderline Besov norms with d ≥ 3. Moreover, u has a uniq...In this paper, we shall prove that the Koch-Tataru solution u to the incompressible Navier-Stokes equations in Rd satisfies the decay estimates involving some borderline Besov norms with d ≥ 3. Moreover, u has a unique trajectory which is HSlder continuous with respect to the space variables.展开更多
基金Acknowledgements We are very grateful to the referee＇s suggestions and comments on the improvement of the paper. Part of this work was done when we were visiting Morningside Center of Mathematics, Chinese Academy of Sciences, in the summer of 2010. We appreciate the hospitality and the financial support from the center. P. Zhang is partially supported by National Natural Science Foundation of China （Grant Nos. 10421101 and 10931007）, and the innovation grant from the Chinese Academy of Sciences （Grant No. GJHZ200829）. T. Zhang is partially supported by the Program for New Century Excellent Talents in University, National Natural Science Foundation of China （Grant Nos. 10871175, 10931007 and 10901137）, and the Zhejiang Provincial Natural Science Foundation of China （Grant No. Z6100217）.
文摘In this paper, we shall prove that the Koch-Tataru solution u to the incompressible Navier-Stokes equations in Rd satisfies the decay estimates involving some borderline Besov norms with d ≥ 3. Moreover, u has a unique trajectory which is HSlder continuous with respect to the space variables.
