ترغب بنشر مسار تعليمي؟ اضغط هنا

A regularity criterion for the dissipative quasi-geostrophic equations

103   0   0.0 ( 0 )
 نشر من قبل Hongjie Dong
 تاريخ النشر 2007
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We establish a regularity criterion for weak solutions of the dissipative quasi-geostrophic equations in mixed time-space Besov spaces.



قيم البحث

اقرأ أيضاً

410 - M.Cannone , C. Miao , L.Xue 2011
We consider the 2D quasi-geostrophic equation with supercritical dissipation and dispersive forcing in the whole space. When the dispersive amplitude parameter is large enough, we prove the global well-posedness of strong solution to the equation wit h large initial data. We also show the strong convergence result as the amplitude parameter goes to $infty$. Both results rely on the Strichartz-type estimates for the corresponding linear equation.
168 - Daoyuan Fang , Chenyin Qian 2012
In this article, we establish sufficient conditions for the regularity of solutions of Navier-Stokes equations based on one of the nine entries of the gradient tensor. We improve the recently results of C.S. Cao, E.S. Titi (Arch. Rational Mech.Anal. 202 (2011) 919-932) and Y. Zhou, M. Pokorn$acute{y}$ (Nonlinearity 23, 1097-1107 (2010)).
67 - Tsukasa Iwabuchi 2021
We study the Cauchy problem for the quasi-geostrophic equations with the critical dissipation in the two dimensional half space under the homogeneous Dirichlet boundary condition. We show the global existence, the uniqueness and the analyticity of so lutions, and the real analyticity up to the boundary is obtained. We will show one of natural ways to estimate the nonlinear term for functions satisfying the Dirichlet boundary condition.
156 - Daoyuan Fang , Chenyin Qian 2012
Several regularity criterions of Leray-Hopf weak solutions $u$ to the 3D Navier-Stokes equations are obtained. The results show that a weak solution $u$ becomes regular if the gradient of velocity component $ abla_{h}{u}$ (or $ abla{u_3}$) satisfies the additional conditions in the class of $L^{q}(0,T; dot{B}_{p,r}^{s}(mathbb{R}^{3}))$, where $ abla_{h}=(partial_{x_{1}},partial_{x_{2}})$ is the horizontal gradient operator. Besides, we also consider the anisotropic regularity criterion for the weak solution of Navier-Stokes equations in $mathbb{R}^3$. Finally, we also get a further regularity criterion, when give the sufficient condition on $partial_3u_3$.
We are concerned with the existence of periodic travelling-wave solutions for the generalized surface quasi-geostrophic (gSQG) equation(including incompressible Euler equation), known as von Karman vortex street. These solutions are of $C^1$ type, an d are obtained by studying a semilinear problem on an infinite strip whose width equals to the period. By a variational characterization of solutions, we also show the relationship between vortex size, travelling speed and street structure. In particular, the vortices with positive and negative intensity have equal or unequal scaling size in our construction, which constitutes the regularization for Karman point vortex street.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا