In this paper, we consider the logarithmically improved regularity criterion for the supercritical quasi-geostrophic equation in Besov space B ∞,∞ -r （R2）. The result shows that if 0 is a weak solutions satisfies ...In this paper, we consider the logarithmically improved regularity criterion for the supercritical quasi-geostrophic equation in Besov space B ∞,∞ -r （R2）. The result shows that if 0 is a weak solutions satisfies ∫ 0 T ｜｜ θ （·,s）｜｜a/a-r B ∞,∞ -r /（1＋ln（e＋｜｜ ⊥（·,s）｜｜ L r2） ds〈∞ for some 0〈r〈a and 0〈a〈1,then θ is regular at t = T. In view of the embedding L 2/r M p 2/r B ∞,∞ -r with 2≤p〈2/r and 0≤r〈1, we see that our result extends the results due to [20] and [31].展开更多
文摘In this paper, we consider the logarithmically improved regularity criterion for the supercritical quasi-geostrophic equation in Besov space B ∞,∞ -r （R2）. The result shows that if 0 is a weak solutions satisfies ∫ 0 T ｜｜ θ （·,s）｜｜a/a-r B ∞,∞ -r /（1＋ln（e＋｜｜ ⊥（·,s）｜｜ L r2） ds〈∞ for some 0〈r〈a and 0〈a〈1,then θ is regular at t = T. In view of the embedding L 2/r M p 2/r B ∞,∞ -r with 2≤p〈2/r and 0≤r〈1, we see that our result extends the results due to [20] and [31].
