在 [Berselli, Luigi C.; Córdoba, Diego. On the regularity of the solutions to the 3D Navier-Stokes equations: a remark on the role of the helicity. C. R. Math. Acad. Sci. Paris 347 (2009), no. 11-12, 613--618] 中, 作者证明了如果$$|u(x+y,t)\cdot \om(x,t)|\leq…
在 [Chae, Dongho. On the regularity conditions of suitable weak solutions of the 3D Navier-Stokes equations. J. Math. Fluid Mech. 12 (2010), no. 2, 171--180] 中, 作者证明了如果$$u\times\f{\om}{|\om|}\in L^p(0,T;L^q(\bbR^3)),\quad\f{2}{p}+\f{3}{q}=1,\quad 3<q\…
In [Zhang, Zujin. Serrin-type regularity criterion for the Navier-Stokes equations involving one velocity and one vorticity component. Czechoslovak Math. J. 68 (2018), no. 1, 219--225], we give an affirmative answer to an open problem in [Penel, Patr…
Cross Product These are two vectors: They can be multiplied using the "Cross Product" (also see Dot Product) The Cross Product a × b of two vectors is another vector that is at right angles to both: And it all happens in 3 dimensions! Calculatin…
In [Zujin Zhang, Jinlu Li, Zheng-an Yao, A remark on the global regularity criterion for the 3D Navier-Stokes equations based on end-point Prodi-Serrin conditions, Applied Mathematics Letters, 83 (2018), 182—187], we take full advantage of the regula…
In [Zhang, Zujin; Yao, Zheng-an. 3D axisymmetric MHD system with regularity in the swirl component of the vorticity. Comput. Math. Appl. 73 (2017), no. 12, 2573--2580], we have obtained the following fine property of the convective terms of axisymmet…
In [Zhang, Zujin. An improved regularity criterion for the Navier–Stokes equations in terms of one directional derivative of the velocity field. Bull. Math. Sci. 8 (2018), no. 1, 33--47] we have improved the results in Kukavica and Ziane (J Math Phys…
向量 dot cross product 点积叉积 几何意义 有向量 a b 点积 a * b = |a| * |b| * cosθ 几何意义: 1. a * b == 0,则 a ⊥ b 2. a * b > 0,a b 同向 3. a * b < 0,a b 异向 4. 我们可以 normalize a 和 b,则 |a|,|b| 都为1,那么 cosθ = a*b,在知道 cosθ 的情况下,我们可以求知 a 在 b 上的投射长度 |a| * cosθ,b 在 a 上的投射长度 |b|…
