Year: 2025
Type: article
Abstract: We study solutions, with scaling-invariant bounds, to the steady simplified Ericksen-Leslie system in R n ∖ { 0 } \mathbb {R}^n\setminus \{0\} . When n = 2 n=2 , we construct and classify a class of self-similar solutions. When n ≥ 3 n\ge 3 , we establish the rigidity asserting that if ( u , d ) (u,d) satisfies a scaling-invariant bound with a small constant, then u ≡ 0 u\equiv 0 and d = d= constant for n ≥ 4 n\geq 4 or u u is a Landau solution and d = d= constant for n = 3 n=3 . Such a smallness condition can be weaken when n = 4 n=4 or the solutions are self-similar.
DOI: 10.1090/proc/17384
Authors: Jeaheang Bang, Changyou Wang
Institutions: Westlake University, Purdue University West Lafayette
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415308977