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Remarks on the a priori bound for the vorticity of the axisymmetric Navier-Stokes equations

Zujin Zhang, Chenxuan Tong (2022)

Applications of Mathematics

We study the axisymmetric Navier-Stokes equations. In 2010, Loftus-Zhang used a refined test function and re-scaling scheme, and showed that $| ω^{r} (x, t) | + | ω^{z} (r, t) | \leq \frac{C}{r^{10}}, 0 < r \leq \frac{1}{2} .$ By employing the dimension reduction technique by Lei-Navas-Zhang, and analyzing $ω^{r}$ , $ω^{z}$ and $ω^{θ} / r$ on different hollow cylinders, we are able to improve it and obtain $| ω^{r} (x, t) | + | ω^{z} (r, t) | \leq \frac{C | \ln r |}{r^{17 / 2}}, 0 < r \leq \frac{1}{2} .$

Remarks on the blow-up criterion for the MHD system involving horizontal components or their horizontal gradients

Zujin Zhang, Xian Yang (2016)

Annales Polonici Mathematici

We study the Cauchy problem for the MHD system, and provide two regularity conditions involving horizontal components (or their gradients) in Besov spaces. This improves previous results.

Displaying 81 – 90 of 90

Remarks on the a priori bound for the vorticity of the axisymmetric Navier-Stokes equations

Remarks on the blow-up criterion for the MHD system involving horizontal components or their horizontal gradients

Remarks on the Regularity of Weak Solutions to Some Variational Inequalities.

Remarks on the smoothness of the $L^{\infty} (0, T; L^{3})$ solutions of the 3-D Navier-Stokes equations.

Removable singularities for weak solutions of quasilinear elliptic systems.

Removeable singular sets of fully nonlinear elliptic equations.

Reverse smoothing effects, fine asymptotics, and Harnack inequalities for fast diffusion equations.

Riesz transform on manifolds and heat kernel regularity

Risultati di esistenza, regolarità e confronto per equazioni ellittiche

Risultati di regolarità, stabilità, instabilità e biforcazione per un problema a frontiera libera

Currently displaying 81 – 90 of 90