Jie Xin

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math.AP2026

Global regularity and general-coefficient singular limits for energy-critical complex Ginzburg--Landau equations

Lingbang Gao, Jie Xin, Yunrui Zheng

We study energy-critical complex Ginzburg--Landau equations with a linear damping term $R u$ , $R \geq 0$ . For the undamped aligned equation in dimensions $d = 3, 4$ , we treat the focusi…

math.AP2025

$(H, H^{2})$ -smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus

Hongyong Cui, Hui Liu, Jie Xin

This paper is devoted to the regularity of Navier-Stokes (NS) equations with additive white noise on two-dimensional torus $T^{2}$ . Under the conditions that the external for…

math.AP2025

$(H, H^{3})$ -smoothing effect and convergence of solutions of stochastic two-dimensional anisotropic Navier-Stokes equations driven by colored noise

Hui Liu, Dong Su, Chengfeng Sun +1

This paper is devoted to the higher regularity and convergence of solutions of anisotropic Navier-Stokes (NS) equations with additive colored noise and white noise on two-dimension…

math.AP2025

Regularity of random attractor and fractal dimension of fractional stochastic Navier-Stokes equations on three-dimensional torus

Hui Liu, Chengfeng Sun, Jie Xin

In this paper we will study the asymptotic dynamics of fractional Navier-Stokes (NS) equations with additive white noise on three-dimensional torus $T^{3}$ . Under the conditi…

Global regularity and general-coefficient singular limits for energy-critical complex Ginzburg--Landau equations

(H,H2)-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus

(H,H3)-smoothing effect and convergence of solutions of stochastic two-dimensional anisotropic Navier-Stokes equations driven by colored noise

Regularity of random attractor and fractal dimension of fractional stochastic Navier-Stokes equations on three-dimensional torus

$(H, H^{2})$ -smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus

$(H, H^{3})$ -smoothing effect and convergence of solutions of stochastic two-dimensional anisotropic Navier-Stokes equations driven by colored noise