Let u = （Uh,U3） be a smooth solution of the 3-D Navier-Stokes equations in R3 × [0, T）. It was proved that if u3 ∈ L^∞（0,T;Bp,q-1＋3/p（R3）） for 3 〈 p,q 〈 oe and uh ∈ L^∞（0, T;BMO-1（R3）） with uh（...Let u = （Uh,U3） be a smooth solution of the 3-D Navier-Stokes equations in R3 × [0, T）. It was proved that if u3 ∈ L^∞（0,T;Bp,q-1＋3/p（R3）） for 3 〈 p,q 〈 oe and uh ∈ L^∞（0, T;BMO-1（R3）） with uh（T） ∈ VMO-1（R3）, then u can be extended beyond T. This result generalizes the recent result proved by Gallagher et al. （2016）, which requires u ∈ L^∞（O,T;Bp,^-11＋3/P（R3））. Our proof is based on a new interior regularity criterion in terms of one velocity component, which is independent of interest.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11301048, 11371039 and 11425103)the Fundamental Research Funds for the Central Universities
文摘Let u = （Uh,U3） be a smooth solution of the 3-D Navier-Stokes equations in R3 × [0, T）. It was proved that if u3 ∈ L^∞（0,T;Bp,q-1＋3/p（R3）） for 3 〈 p,q 〈 oe and uh ∈ L^∞（0, T;BMO-1（R3）） with uh（T） ∈ VMO-1（R3）, then u can be extended beyond T. This result generalizes the recent result proved by Gallagher et al. （2016）, which requires u ∈ L^∞（O,T;Bp,^-11＋3/P（R3））. Our proof is based on a new interior regularity criterion in terms of one velocity component, which is independent of interest.
