arXiv subjects
Publications and source records attributed to Sadek Gala.
In this paper, we study regularity of weak solutions to the incompressible Navier-Stokes equations in $\mathbb{R}^{3}\times (0,T)$. The main goal is to establish the regularity criterion via the gradient of one velocity component in multiplier spaces.
This work focuses on the 3D incompressible magnetohydrodynamic (MHD) equations with mixed pressure-velocity-magnetic field in view of Lorentz spaces. Our main result shows the weak solution is regular, provided that $${\frac{π}{\left( e^{-\left\vert x\right\vert ^{2}}+\left\vert u\right\vert +\left\vert b\right\vert \right) ^{θ}}\in L}^{p}(0,T;L^{q,\infty }(\mathbb{R}^{3})),\text{ where }\frac{2}{p}+\frac{3}{% q}=2-θ\text{ and }0\leq θ\leq 1.$$
This paper has been removed by arXiv administrators because it plagiarizes math.AP/0501483, "Quasilinear and Hessian equations of Lane-Emden type" by Nguyen Cong Phuc and Igor E. Verbitsky.
This paper was removed by arXiv admin because it plagiarizes the electronic article HYKE 2005-010 (http://www.hyke.org/preprint/index.php), by Jose-A. Carrillo and Lucas C.f. Ferreira, entitled "Self-similar solutions and large time asymptotics for the dissipative quasi-geostrophic equations".
This paper was removed by arXiv admin because it plagiarizes "Ding, Yong(PRC-BJN); Fan, Dashan(PRC-ANH); Pan, Yibiao(1-PITT) Weighted boundedness for a class of rough Marcinkiewicz integrals. Indiana Univ. Math. J. 48 (1999), no. 3, 1037--1055."
This paper was removed by arXiv admin because it plagiarizes "Kozono, Hideo; Shimada, Yukihiro Bilinear estimates in homogeneous Triebel-Lizorkin spaces and the Navier-Stokes equations. Math. Nachr. 276 (2004), 63--74."
This paper was withdrawn by arXiv admin because it plagiarizes "Chen, Wen Gu(PRC-BIAP); Lu, Shan Zhen(PRC-BJN) The commutators of fractional integrals on Besov spaces. Acta Math. Sin. (Engl. Ser.) 20 (2004), no. 3, 405--414."
In this paper,we will study the boundedness properties of commutator \[ C_{f}=[ f,Δ] \] acting from $\overset{.}{H}^{1}(\mathbb{R}^{d}) $ to $\overset{.}{H}^{-1}(\mathbb{R}^{d}) .$
Let $σ(x,ξ) $ be a sufficiently regular function defined on $R^d \times R^d.$ The pseudo-differential operator with symbol $σ$ is defined on the Schwartz class by the formula: \[f\toσf(x)=\int_{R^d} σ(x,ξ) \hat{f}(ξ)e^{2πixξ}dξ, \] where $\hat{f}(ξ)=\int_{R^d} f(x)e^{-2πixξ}dx$ is the Fourier transform of $f.$ In this paper, we shall consider the regularity of the following type : \begin{description} \item[(a)] $| \partial_ξ^ασ(x,ξ) | \leq A_α(1+| ξ|) ^{-| α|},$ \item[(b)] $| \partial_ξ^ασ(x+y,ξ) -\partial_ξ^ασ(x,ξ) | \leq A_αω(| y|) (1+| ξ|) ^{-| α|},$ \end{description} %