论文标题
OnSager功能的临界点的轴对称性
Axisymmetry of critical points for the Onsager functional
论文作者
论文摘要
一个简单的证据证明了Fatkullin和Slastikov（2005），Liu，Zhang和Zhang（2005）导致的经典结果，即通过Maier-Saupe Molecular互动功能的OnSager功能的关键点是轴心对称性的，包括稳定的关键点，包括额外的偶极 - 二波尔 - 偶极互动（Zhou等2007）。证明避免了球形极坐标，而是使用球体上的积分身份$ s^2 $。对于与绝对连续内核的一般相互作用，所有关键点的平滑度都建立了，从而推广了Vollmer（2016）对Onsager相互作用的结果。还表明，对于包括Onsager的各种相互作用，存在非轴对称临界点。
A simple proof is given of the classical result due to Fatkullin and Slastikov (2005), Liu, Zhang and Zhang (2005) that critical points for the Onsager functional with the Maier-Saupe molecular interaction are axisymmetric, including the case of stable critical points with an additional dipole-dipole interaction (Zhou et al 2007). The proof avoids spherical polar coordinates, instead using an integral identity on the sphere $S^2$. For general interactions with absolutely continuous kernels the smoothness of all critical points is established, generalizing a result of Vollmer (2016) for the Onsager interaction. It is also shown that non-axisymmetric critical points exist for a wide variety of interactions including that of Onsager.
