ترغب بنشر مسار تعليمي؟ اضغط هنا

Global Existence and Regularity for the Active Liquid Crystal System

152   0   0.0 ( 0 )
 نشر من قبل Rongfang Zhang
 تاريخ النشر 2015
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

In this paper, we study the active hydrodynamics, described in the Q-tensor liquid crystal framework. We prove the existence of global weak solutions in dimension two and three, with suitable initial datas. By using Littlewood-Paley decomposition, we also get the higher regularity of the weak solutions and the uniqueness of weak-strong solutions in dimension two.



قيم البحث

اقرأ أيضاً

103 - Zhaoyang Qiu , Yixuan Wang 2020
The global weak martingale solution is built through a four-level approximation scheme to stochastic compressible active liquid crystal system driven by multiplicative noise in a smooth bounded domain in $mathbb{R}^{3}$ with large initial data. The c oupled structure makes the analysis challenging, and more delicate arguments are required in stochastic case compared to the deterministic one cite{11}.
We consider a full Navier-Stokes and $Q$-tensor system for incompressible liquid crystal flows of nematic type. In the two dimensional periodic case, we prove the existence and uniqueness of global strong solutions that are uniformly bounded in time. This result is obtained without any smallness assumption on the physical parameter $xi$ that measures the ratio between tumbling and aligning effects of a shear flow exerting over the liquid crystal directors. Moreover, we show the uniqueness of asymptotic limit for each global strong solution as time goes to infinity and provide an uniform estimate on the convergence rate.
By studying the linearization of contour dynamics equation and using implicit function theorem, we prove the existence of co-rotating and travelling global solutions for the gSQG equation, which extends the result of Hmidi and Mateu cite{HM} to $alph ain[1,2)$. Moreover, we prove the $C^infty$ regularity of vortices boundary, and show the convexity of each vortices component.
134 - Mengyun Liu , Chengbo Wang 2017
In this paper, we prove the global existence for some 4-D quasilinear wave equations with small, radial data in $H^{3}times H^{2}$. The main idea is to exploit local energy estimates with variable coefficients, together with the trace estimates.
The two-dimensional Zakharov system is shown to have a unique global solution for data without finite energy if the L^2 - norm of the Schrodinger part is small enough. The proof uses a refined I-method originally initiated by Colliander, Keel, Staffi lani, Takaoka and Tao. A polynomial growth bound for the solution is also given.
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