3 papers
math.AP2026
Global dynamics and asymptotic stability for a nonlocal LANS--type system
Chunxia Guan, Kai Yan, Qianyuan Zhang
This paper is devoted to the global dynamics of a nonlocal Lagrangian-averaged Navier-Stokes- (LANS-)-type system (also known as the viscous Euler-Poincaré system) in one, tw…
math.AP2026
Sharp well-posedness and ill-posedness of the Camassa-Holm equation in critical Triebel-Lizorkin spaces
Qianyuan Zhang, Kai Yan
This paper is devoted to the sharp well-posedness and ill-posedness of the Cauchy problem for the Camassa-Holm (CH) equation in critical Triebel-Lizorkin spaces $F^{1+\frac{1}{p}}_…
math.AP2026
Commutator estimates and their applications to the transport-type equations
Qianyuan Zhang, Kai Yan
In this paper, we derive new commutator estimates in the Triebel-Lizorkin spaces by employing Bony's para-product decomposition, the Nikol'skij representation, and the Fefferman-St…