2025/02/07 by Bang, Jeaheang, Wang, Changyou
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2502.05326
We study solutions, with scaling-invariant bounds, to the steady simplified Ericksen-Leslie system in ℝn∖ \0\. When n=2, we construct and classify a class of self-similar solutions. When n≥ 3, we establish the rigidity asserting that if (u,d) satisfies a scaling-invariant bound with a small constant, then u≡ 0 and d= constant for n≥ 4 or u is a Landau solution and d= constant for n=3. Such a smallness condition can be weaken when n=4 or the solutions are self-similar.