跟锦数学

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[科研] (170722) 对速度 $u=(u_1,u_2,u_3)$, 其旋度定义为 $$\bex \bbom=\n\times \bbu=(\p_2u_3-\p_3u_2,\p_3u_1-\p_1u_3,\p_1u_2-\p_2u_1). \eex$$ 而有公式... zhangzujin 2018-1-3 0104 zhangzujin 2018-1-3 12:47
[科研] (170605) Let $$\beex \bea \lm,\mu\in\bbR,\quad 1\leq p,q\leq r\leq \infty,\quad 0<\tt<1,\\ -\lm+\frac{n}{p}<\frac{n}{r}<-\mu+\frac{n}{q},\\ \frac{n}{r}=(1-\tt)\sex{-\lm+\frac{n}{p}} +\tt\sex{-\mu+\frac{n}{q}}. \eea \eeex$$Then ... zhangzujin 2017-7-8 084 zhangzujin 2017-7-8 09:40
[科研] 70603) $$\bex \dot B^0_{\infty,2}\subsetneq BMO. \eex$$ zhangzujin 2017-7-8 063 zhangzujin 2017-7-8 09:39
[科研] (170602) $$\bex \n\cdot\bbb=0\ra \n\times [(\n\times \bbb)\times \bbb]=\n\times [\n\cdot (\bbb\otimes \bbb)]. \eex$$ zhangzujin 2017-7-8 0111 zhangzujin 2017-7-8 09:37
[科研] (170601) $$\bex 0<p<\infty\ra H_p=\dot F^0_{p,2};\quad BMO=\dot F^0_{\infty,2}. \eex$$ see [H. Triebel, Theory of function spaces I, Birkh\"auser, Basel, 1983] Page 244 zhangzujin 2017-7-8 083 zhangzujin 2017-7-8 09:36
[科研] (170531) $$\bex \n\times(\bba\times\bbb)=(\bbb\cdot\n)\bba -(\bba\cdot\n)\bbb+\bba(\n\cdot\bbb)-\bbb(\n\cdot\bba). \eex$$ zhangzujin 2017-7-8 059 zhangzujin 2017-7-8 09:34
[科研] (170509) $$\bex (\n\times\bbb)\times\bbb=-\n\frac{|\bbb|^2}{2}+(\bbb\cdot\n)\bbb. \eex$$ zhangzujin 2017-7-8 055 zhangzujin 2017-7-8 09:15
[科研] (170508) For $f\in H^s(\bbR^3)$ with $s>\frac{3}{2}$, we have $$\bex \sen{f}_{L^\infty}\leq C\sex{1+\sen{f}_{\dot B^0_{\infty,\infty}}}\ln \sex{1+\sen{f}_{H^s}},\quad s>\frac{3}{2}. \eex$$ zhangzujin 2017-7-8 068 zhangzujin 2017-7-8 09:13
[科研] (170507) Assume that $a$ is a positive constant, $x(t),y(t)$ are two nonnegative $C^1(\bbR^+)$ functions, and $D(t)$ is a nonnegative function, satisfying $$\bex \frac{\rd}{\rd t} (x^2+y^2)+D \leq a(x^2+y^2+x+y)D. \eex$$ ... zhangzujin 2017-7-8 068 zhangzujin 2017-7-8 09:12
[科研] (170506) $$\bex \sum_{|\al|\leq m}\sen{D^\al (fg)-(D^\al f)g}_{L^2} \leq C\sex{\sen{f}_{L^\infty}\sen{g}_{H^m}+\sen{f}_{H^{m-1}}\sen{\n g}_{L^\infty}}. \eex$$ zhangzujin 2017-7-8 053 zhangzujin 2017-7-8 09:11
[科研] (170425) For $2<q<\infty$, $$\beex \bea -\int \lap \bbu \cdot |\bbu|^{q-2}\bbu ... \eea \eeex$$ zhangzujin 2017-7-8 061 zhangzujin 2017-7-8 08:53
[科研] (170421) $$\beex \bea \int \lap f|f|^{q-2}f\rd x &=...\eea \eeex$$ zhangzujin 2017-7-8 049 zhangzujin 2017-7-8 08:49
[科研] (170416) 如果 $$\bex \sen{\n^2 u_n}_{L^\infty(0,T;L^2(\Om))}\leq C, \eex$$ 则 $$\bex \sen{\n^2 u_n}_{L^2(\Om\times (0,T))}\leq C, \eex$$ 而有子列弱收敛 $$\bex \n^2u_{n_k}\rightharpoonup \n^2u,\mbox{ in }L^2(\Om\times (0,T)). \eex$$ zhangzujin 2017-7-8 085 zhangzujin 2017-7-8 08:44
[科研] (170310) A represented matroid is a pair $M=(E,U)$ consisting of a finite set $E$ together with a subspace $U$ of $\bbF^E$. We say that a matrix $A$ generates a represented matroid $M=(E,U)$ if $U$... zhangzujin 2017-7-7 050 zhangzujin 2017-7-7 16:52
[科研] (170128) 设 $X$ 是 Banach 空间, $f$ 是 $X^2$ 到 $X$ 的双线性映射. 若 $$\bex \exists\ 0<\al<\f{1}{4\sen{f}},\quad \sen{f} =\sup_{\sen{u},\sen{v}\leq 1} \sen{f(u,v)}, \eex$$ 则 ... zhangzujin 2017-7-6 059 zhangzujin 2017-7-6 19:35
[科研] (170127) Liu Y, Zhang P. On the global well-posedness of 3-D axi-symmetric Navier-Stokes system with small swirl component[J]. arXiv preprint arXiv:1702.06279, 2017. zhangzujin 2017-7-6 057 zhangzujin 2017-7-6 19:34
[科研] (170118) Chen, Qionglei; Miao, Changxing. Existence theorem and blow-up criterion of the strong solutions to the two-fluid MHD equation in $\Bbb R^3$. J. Differential Equations 239 (2007), no. 1, 251--271. zhangzujin 2017-7-6 036 zhangzujin 2017-7-6 19:22
[科研] (170117) Tran, Chuong V.; Yu, Xinwei. Note on Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes equations. J. Math. Phys. 58 (2017), no. 1, 011501, 10 pp. zhangzujin 2017-7-6 042 zhangzujin 2017-7-6 19:22
[科研] (170116) Ru, Shaolei; Chen, Jiecheng. Global solution of the 3D incompressible Navier–Stokes equations in the Besov spaces $\dot{R}_{r_1,r_2,r_3}^{\sigma,1}$. Z. Angew. Math. Phys. 68 (2017), no. 2, 68:30. zhangzujin 2017-7-6 026 zhangzujin 2017-7-6 19:21
[科研] (170114) Fan, Jishan; Ahmad, Bashir; Hayat, Tasawar; Zhou, Yong. On blow-up criteria for a new Hall-MHD system. Appl. Math. Comput. 274 (2016), 20--24. zhangzujin 2017-7-6 047 zhangzujin 2017-7-6 19:20
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