Global Low-Energy Weak Solution and Large-Time Behavior for the Compressible Flow of Liquid Crystals

We consider the weak solution of the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in $\mathbb R^3$. When the initial data is small in $L^2$ and initial density is positive and essentially bounded, we first prove the existence of a global weak solution in $\mathbb R^3$. The large-time behavior of a global weak solution is also established.Comment: arXiv admin note: text overlap with arXiv:1110.0053, arXiv:1004.4749 by other author

The Epsilon-Expansion from Conformal Field Theory

Conformal multiplets of $\phi$ and $\phi^3$ recombine at the Wilson-Fisher fixed point, as a consequence of the equations of motion. Using this fact and other constraints from conformal symmetry, we reproduce the lowest nontrivial order results for the anomalous dimensions of operators, without any input from perturbation theory.Comment: 24 pages; v2 - references added, minor changes; v3 - refs and comments added, misprints corrected, version to appear in J.Phys.