arXiv subjects

Lvqiao Liu

Publications and source records attributed to Lvqiao Liu.

4 recordsLinked to original sources

arXiv2026

Sharp decay characterization for the incompressible Oldroyd-B model in critical $L^p$ spaces

This paper establishes a sharp characterization of temporal decay rates for the incompressible Oldroyd-B model in a critical $L^p$ framework, covering the physically relevant and mathematically delicate case where both the fluid viscosity and the stress tensor damping are absent. We prove that an $L^2$-type condition on the low-frequencies part of the initial data $(u_0, τ_0)$ is almost both necessary and sufficient for obtaining optimal upper and lower bounds on the temporal decay of solutions in critical Besov spaces. A key contribution is a new decomposition of the stress tensor into its incompressible and compressible parts, combined with the introduction of an effective tensor to handle the loss of regularity in the high-frequencies velocity field. This is the first result to reveal such precise two-sided asymptotics for the incompressible Oldroyd-B model without viscosity or damping.

math.AP↗

arXiv2026

On the radius of analyticity and Gevrey regularity for the Boltzmann equation

This paper investigates the non-cutoff Boltzmann equation for hard potentials in a perturbative setting. We first establish a sharp short-time estimate on the radius of analyticity and Gevrey regularity of mild solutions. Furthermore, we obtain a global-in-time radius estimate in Gevrey space. The proof combines hypoelliptic estimates with the macro-micro decomposition.

math.AP↗

arXiv2021

Gevrey regularity of mild solutions to the non-cutoff Boltzmann equation

In the paper, for the Cauchy problem on the non-cutoff Boltzmann equation in torus, we establish the global-in-time Gevrey smoothness in velocity and space variables for a class of low-regularity mild solutions near Maxwellians with the Gevrey index depending only on the angular singularity. This together with [24] provides a self-contained well-posedness theory for both existence and regularity of global solutions for initial data of low regularity in the framework of perturbations. For the proof we treat in a subtle way the commutator between the regularization operators and the Boltzmann collision operator involving rough coefficients, and this enables us to combine the classical Hörmander's hypoelliptic techniques together with the global symbolic calculus established for the linearized Boltzmann operator so as to improve the regularity of solutions at positive time.

math.AP↗

arXiv2020

Global well-posedness for the Hall-magnetohydrodynamics system in larger critical Besov spaces

We prove the global well-posedness of the Cauchy problem to the 3D incompressible Hall-magnetohydrodynamic system supplemented with initial data in critical Besov spaces, which generalize the result in [10]. Meanwhile , we analyze the long-time behavior of the solutions and get some decay estimates. Finally, a stability theorem for global solutions is established.

math.AP↗