On the Long Time Dynamics of the Landau-De Gennes Gradient Flow
On the Long Time Dynamics of the Landau-De Gennes Gradient Flow
复制标题
论Landau-De Gennes梯度流的长期动力学
DOI：
10.1007/s10955-022-03046-7
复制
发表时间：
2023
影响因子：
1.6
通讯作者：
Stefanov, Atanas G.
中科院分区：
文献类型：
--
作者：
Stanislavova, Milena;Stefanov, Atanas G.
我们研究了由Landau-de Gennes能量泛函在物理相关的空间维度中产生的梯度流。我们建立了大数据在2D情形下的全局适定性和全局指数时间衰减界，以及在3D情形下的一致界。这确实是3D中无限制系数的最佳可能结果，因为确实存在稳定状态，至少对于某些系数配置是这样。我们还建立了2D中上述动力学的先导阶项，特别是精确的渐近性。在3D中，我们类似地分离前导阶项，在必要的假设下，给定的可能大的解收敛到零。作为推论，我们证明了相关泛函c(y，t)=∫Rdtr(q(x+y，t)q(x，t))dx∫Rdtr(q2(x，t))dx=e-|y|28t+oly∞(t-12)，d=2，3的一个渐近公式。这样的公式在Kirr(J Stat Phys 155：625-657(2014))中被建立，适用于满足非简并条件的小初始数据。
We study the gradient flow, generated by the Landau-De Gennes energy functional, in the physically relevant spatial dimensions. We establish global well-posedness and global exponential time decay bounds for largedata in the 2D case, and uniform bounds for large data in 3D. This is indeed the best possible outcome for unrestricted coefficients in 3D, given that steady states do exist, at least for some coefficient configurations. We also establish leading order terms and in particular sharp asymptotics for the said dynamics in 2D. In 3D, we similarly isolate the leading order term, under the necessary assumption that a given, possibly large, solution converges to zero as. As a corollary, we prove an asymptotic formula for the correlation functional, c(y,t)=∫Rdtr(Q(x+y,t)Q(x,t))dx∫Rdtr(Q2(x,t))dx=e-|y|28t+OLy∞(t-12),d=2,3 for (potentially large) solutionsobeying a natural asymptotic condition. Such a formula was established in Kirr (J Stat Phys 155:625–657 (2014) forand small initial data, subject to the non-degeneracy condition.
R2 上纳维-斯托克斯方程和涡度方程的不变流形和长时间渐近性
影响因子：
2.5
作者：
Thierry GallayUniversit
通讯作者：
Thierry GallayUniversit