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Wanwan Zhang

Publications and source records attributed to Wanwan Zhang.

8 recordsLinked to original sources
arXiv2026

EgoLive: A Large-Scale Egocentric Dataset from Real-World Human Tasks

The advancement of robot learning is currently hindered by the scarcity of large-scale, high-quality datasets. While established data collection methods such as teleoperation and universal manipulation interfaces dominate current datasets, they suffer from inherent limitations in scalability and real-world deployability. Human egocentric video collection, by contrast, has emerged as a promising approach to enable scalable, natural and in-the-wild data collection. As such, we present EgoLive, a large-scale, high-quality egocentric dataset designed explicitly for robot manipulation learning. EgoLive establishes three distinctive technical advantages over existing egocentric datasets: first, it represents the largest open-source annotated egocentric dataset focused on real-world task-oriented human routines to date; second, it delivers leading data quality via a customized head-mounted capture device and comprehensive high-precision multi-modal annotations; third, all data is collected exclusively in unconstrained real-world scenarios and encompasses vertical field human working data, including home service, retail, and other practical work scenarios, providing superior diversity and ecological validity. With the introduction of EgoLive, we aim to provide the research community with a scalable, high-quality dataset that accelerates breakthroughs in generalizable robotic models and facilitates the real-world deployment of robot systems.

cs.RO↗
arXiv2025

Finite time blow-up for a multi-dimensional model of the Kiselev-Sarsam equation

In this paper, we propose and study a multi-dimensional nonlocal active scalar equation of the form \begin{eqnarray*} \partial_t\rho+g\mathcal{R}_a\rho\cdot \nabla\rho= 0,~\rho(\cdot,0)=\rho_{0}, \end{eqnarray*} where the transform $\mathcal{R}_a$ is defined by \begin{eqnarray*} \mathcal{R}_af(x)=\frac{\Gamma(\frac{n+1}{2})}{\pi^{\frac{n+1}{2}}}P.V.\int\limits_{\mathbb{R}^n}\Big(\frac{x-y}{|x-y|^{n+1}}-\frac{x-y}{(|x-y|^2+a^2)^{\frac{n+1}{2}}}\Big)f(y)dy. \end{eqnarray*} This model can be viewed as a natural generalization of the well-known Kiselev-Sasarm equation, which was introduced in [19] as a one-dimensional model for the two-dimensional incompressible porous media equation. We show the local well-posedness for this multi-dimensional model as well as the gradient blow-up in finite time for a class of radial initial data.

math.AP↗
arXiv2025

On a 1D nonlocal transport of the incompressible porous media equation

Recently, Kiselev and Sarsam proposed the following nonlocal transport equation as a one-dimensional analogue of the 2D incompressible porous media (IPM) equation \begin{eqnarray*} \partial_t\rho+u\partial_x\rho= 0,~u=gH_a\rho, \end{eqnarray*} where the transform $H_a$ is defined by \begin{eqnarray*} H_af(x)=\frac{1}{\pi}P.V.\int\limits_{\mathbb{R}}\frac{a^2f(y)}{(x-y)((x-y)^2+a^2)}dy. \end{eqnarray*} In the work Kiselev-Sarsam (2025) [14], the authors proved the local well-posedness for this 1D periodic IPM model as well as finite time blow-up for a class of smooth initial data. In this paper, we present several new weighted inequalities for the transform $H_a$ in the setting of the real line. Based on these integral inequalities, we also prove the finite time blow-up for this 1D IPM model on the real line.

math.AP↗
arXiv2024

On a multi-dimensional transport equation with nonlocal velocity and fractional dissipation

This paper aims to investigate a multi-dimensional transport equation with nonlocal velocity and fractional dissipation.The balance between the nonlinearity and dissipation gives rise to three different cases, namely the subcritical, critical and supercritical ranges. We study those three cases and obtain a set of results containing local well-posedness, global smoothness, eventual regularity and finite-time blowup of smooth solutions.

math.AP↗
arXiv2024

On the blowup of solutions for a nonlocal multi-dimensional transport equation

In this paper, we revisit the problem of finite-time blowup for a multi-dimensional nonlocal transport equation studied in [Dong, Adv. Math. 264 (2014) 747-761]. Inspired by a one-dimensional analogous model considered in [Li-Rodrigo, Adv. Math. 374 (2020) 1-26], we establish a new weighted nonlinear inequality implying the blow-up by a completely real variable based technique. In particular, an inequality for the Riesz transform is obtained.

math.AP↗
arXiv2021

Global well-posedness to the two-dimensional incompressible vorticity equation in the half plane

This paper is concerned with the global well-posedness of the two-dimensional incompressible vorticity equation in the half plane. Under the assumption that the initial vorticity $ω_0\in W^{k,p}(\R^{2}_+)$ with $k\geq3$ and $1 0$. An elementary and self-contained proof is presented and delicate estimates of the velocity and its derivatives are obtained in this paper. It should be emphasized that the uniform estimate on $\int^t_0\|u(τ)\|_{W^{1,\infty}(\R^2_+)}dτ$ is required to complete the global regularity of the solution. To do that, the double exponential growth in time of the gradient of the vorticity in the half plane is established and applied. This is different from the proof of global well-posedness of the Euler velocity equations in the Sobolev spaces, in which a Kato-type or logarithmic-type estimate of the gradient of the velocity is enough to close the energy estimates.

math.AP↗
arXiv2021

Local Well-posedness of Two Dimensional SQG Equation and Related Models

In this paper, we present a new and elementary proof of the local existence and uniqueness of the classical solution to the Cauchy problem of the two-dimensional generalized surface quasi-geostrophic (SQG) equation via the method of the contraction mapping principle. Also, same result holds true for a kind of transport equation with nonlocal velocity via the method of the contraction mapping principle.

math.AP↗