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Yulin Ye

Publications and source records attributed to Yulin Ye.

At least 19 recordsLinked to original sources
arXiv2025

On anisotropic energy conservation criteria of incompressible fluids

In this paper, by means of divergence-free condition, we establish an anisotropic energy conservation class enabling one component of velocity in the largest space $L^{3} (0,T; B^{1/3}_{3,\infty})$ for the 3D inviscid incompressible fluids, which extends the celebrated result obtained by Cheskidov, Constantin, Friedlander and Shvydkoy in [15, Nonlinearity 21 (2008)]. For viscous flows, we generalize famous Lions's energy conservation criteria to allow the horizontal components and vertical part of velocity to have different integrability.

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arXiv2025

A note on helicity conservation for compressible Euler equations in a bounded domain with vacuum

In this paper, we consider the helicity conservation of weak solutions for the compressible Euler equations in a bounded domain with general pressure law and vacuum. We deduce a sufficient condition for a weak solution conserving the helicity based on the interior Besov-VMO type regularity, the continuous conditions for velocity and vorticity near the boundary, and some regularities for density near vacuum.

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arXiv2025

Boosting the Transferability of Audio Adversarial Examples with Acoustic Representation Optimization

With the widespread application of automatic speech recognition (ASR) systems, their vulnerability to adversarial attacks has been extensively studied. However, most existing adversarial examples are generated on specific individual models, resulting in a lack of transferability. In real-world scenarios, attackers often cannot access detailed information about the target model, making query-based attacks unfeasible. To address this challenge, we propose a technique called Acoustic Representation Optimization that aligns adversarial perturbations with low-level acoustic characteristics derived from speech representation models. Rather than relying on model-specific, higher-layer abstractions, our approach leverages fundamental acoustic representations that remain consistent across diverse ASR architectures. By enforcing an acoustic representation loss to guide perturbations toward these robust, lower-level representations, we enhance the cross-model transferability of adversarial examples without degrading audio quality. Our method is plug-and-play and can be integrated with any existing attack methods. We evaluate our approach on three modern ASR models, and the experimental results demonstrate that our method significantly improves the transferability of adversarial examples generated by previous methods while preserving the audio quality.

cs.SD↗
arXiv2024

Four-fifths laws in incompressible and magnetized fluids: Helicity, Energy and Cross-helicity

In this paper, we are concerned with the Kolmogorov's scaling laws of conserved quantities. By means of Eyink's longitudinal structure functions and the analysis of interaction of different physical quantities, we extend celebrated four-fifths laws from energy to helicity in incompressible fluid and, energy and cross-helicity in magnetohydrodynamic flow. In contrast to pervious 4/5 laws of energy and cross-helicity in magnetized fluids obtained by Politano and Pouquet, they are in terms of the mixed three-order structure functions rather than the structure coupling correlation functions.

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arXiv2023

On the energy and helicity conservation of the incompressible Euler equations

In this paper, we are concerned with the minimal regularity of weak solutions implying the law of balance for both energy and helicity in the incompressible Euler equations. In the spirit of recent works due to Berselli [5] and Berselli-Georgiadis [6], it is shown that the energy of weak solutions is invariant if $v\in L^{p}(0,T;B^{\frac1p}_{\frac{2p}{p-1},c(\mathbb{N})} )$ with $1<p\leq3$ and the helicity is conserved if $v\in L^{p}(0,T;B^{\frac2p}_{\frac{2p}{p-1},c(\mathbb{N})} )$ with $2<p\leq3 $ for both the periodic domain and the whole space, which generalizes the classical work of Cheskidov-Constantin-Friedlander-Shvydkoy in [10]. This indicates the role of the time integrability, spatial integrability and differential regularity of the velocity in the conserved quantities of weak solutions of the ideal fluid.

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arXiv2023

On two conserved quantities in the inviscid electron and Hall magnetohydrodynamic equations

In this paper, we are concerned with the energy and magnetic helicity conservation of weak solutions for both the electron and Hall magnetohydrodynamic equations. Various sufficient criteria to ensure the energy and magnetic helicity conservation in Onsager's critical spaces $\underline{B}^{\alpha}_{p,VMO}$ and $B^{\alpha}_{p,c(\mathbb{N})}$ in these systems are established. Moreover, for the E-MHD equations, we observe that the conservation criteria of energy and magnetic helicity to the E-MHD equations correspond to the helicity and energy to the ideal incompressible Euler equations, respectively.

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arXiv2023

Yaglom's law and conserved quantity dissipation in turbulence

In this paper, we are concerned with the local exact relationship for third-order structure functions in the temperature equation, the inviscid MHD equations and the Euler equations in the sense of Duchon-Robert type and Eyink type. It is shown that the local version of Yaglom's $4/3$ law is valid for the dissipation rates of conserved quantities such as the energy, cross-helicity and helicity in these systems. In the spirit of Duchon-Robert's classical work, we derive the dissipation term resulted from the lack of smoothness of the solutions in corresponding conservation relation. It seems that these results suggest that the Yaglom's law of the hydrodynamic equations holds if an analogue of dissipation term as Duchon-Robert's is obtained. Base on this, the first Yaglom's relation for the Oldroyd-B model and, inspired by the very recent work due to Boutros-Titi, six new 4/3 laws for subgrid scale $α$-models of turbulence are also presented.

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arXiv2022

Energy and helicity conservation for the generalized quasi-geostrophic equation

In this paper, we consider the 2-D generalized surface quasi-geostrophic equation with the velocity $v$ determined by $v=\mathcal{R}^{\perp}Λ^{γ-1}θ$. It is shown that the $L^p$ type energy norm of weak solutions is conserved provided $θ\in L^{p+1}(0,T; {B}^{\fracγ{3}}_{p+1, c(\mathbb{N})})$ for $0<γ<\frac32$ or $θ\in L^{p+1}(0,T; {B}^α_{p+1,\infty})~\text{for any}~γ-1<α<1 \text{ with} ~\frac{3}{2}\leq γ<2$. Moreover, we also prove that the helicity of weak solutions satisfying $\nablaθ\in L^{3}(0,T;\dot{B}_{3,c(\mathbb{N})}^{\fracγ{3}})$ for $0<γ<\frac32$ or $\nablaθ\in L^{3}(0,T; \dot{B}^α_{3,\infty})~\text{for any}~γ-1<α<1 \text{ with} ~\frac{3}{2}\leq γ<2$ is invariant. Therefore, the accurate relationships between the critical regularity for the energy (helicity) conservation of the weak solutions and the regularity of velocity in 2-D generalized quasi-geostrophic equation are presented.

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arXiv2022

Energy conservation of weak solutions for the incompressible Euler equations via vorticity

Motivated by the works of Cheskidov, Lopes Filho, Nussenzveig Lopes and Shvydkoy in [8, Commun. Math. Phys. 348: 129-143, 2016] and Chen and Yu in [5, J. Math. Pures Appl. 131: 1-16, 2019], we address how the $L^p$ control of vorticity could influence the energy conservation for the incompressible homogeneous and nonhomogeneous Euler equations in this paper. For the homogeneous flow in the periodic domain or whole space, we provide a self-contained proof for the criterion $ω=\text{curl}u\in L^{3}(0,T;L^{\frac{3n}{n+2}}(Ω))\,(n=2,3)$, which generalizes the corresponding result in [8] and can be viewed as in Onsager critical spatio-temporal spaces. Regarding the nonhomogeneous flow, it is shown that the energy is conserved as long as the vorticity lies in the same space as before and $\nabla\sqrtρ$ belongs to $L^{\infty}(0,T;L^{n}(\mathbb{T}^{n}))\,(n=2,3)$, which gives an affirmative answer to a problem proposed by Chen and Yu in [5].

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arXiv2022

Analytical validation of the helicity conservation for the compressible Euler equations

In [25], Moffatt introduced the concept of helicity in an inviscid fluid and examined the helicity preservation of smooth solution to barotropic compressible flow. In this paper, it is shown that the weak solutions of the above system in Onsager type spaces $\dot{B}^{1/3}_{p,c(\mathbb{N})}$ guarantee the conservation of the helicity. The parallel results of homogeneous incompressible Euler equations and the surface quasi-geostrophic equation are also obtained.

math.AP↗
arXiv2022

A general sufficient criterion for energy conservation in the Navier-Stokes system

In this paper, we derive an energy conservation criterion based on a combination of velocity and its gradient for the weak solutions of both the homogeneous incompressible Navier-Stokes equations and the general compressible Navier-Stokes equations. For the incompressible case, this class implies most known corresponding results on periodic domain via either the velocity or its gradient including the famous Lions' energy conservation criterion obtained in \cite{[Lions]}. For the compressible case, this helps us to extend the previously known criteria for the energy conservation of weak solutions from the incompressible fluid to compressible flow and improve the recent results due to Nguyen-Nguyen-Tang in \cite[Nonlinearity 32 (2019)]{[NNT]} and Liang in \cite[Proc. Roy. Soc. Edinburgh Sect. A (2020)]{[Liang]}.

math.AP↗
arXiv2021

Energy equality for the isentropic compressible Navier-Stokes equations without upper bound of the density

In this paper, we are concerned with the minimal regularity of both the density and the velocity for the weak solutions keeping energy equality in the isentropic compressible Navier-Stokes equations. The energy equality criteria without upper bound of the density are established. Almost all previous corresponding results requires $ρ\in L^{\infty}(0,T;L^{\infty}(\mathbb{T}^{d}))$.

math.AP↗
arXiv2021

The role of density in the energy conservation for the isentropic compressible Euler equations

In this paper, we study Onsager's conjecture on the energy conservation for the isentropic compressible Euler equations via establishing the energy conservation criterion involving the density $\varrho\in L^{k}(0,T;L^{l}(\mathbb{T}^{d}))$. The motivation is to analysis the role of the integrability of density of the weak solutions keeping energy in this system, since almost all known corresponding results require $\varrho\in L^{\infty}(0,T;L^{\infty}(\mathbb{T}^{d}))$. Our results imply that the lower integrability of the density $\varrho$ means that more integrability of the velocity $v$ are necessary in energy conservation and the inverse is also true. The proof relies on the Constantin-E-Titi type and Lions type commutators on mollifying kernel.

math.AP↗
arXiv2021

Energy equality in the isentropic compressible Navier-Stokes equations allowing vacuum

It is well-known that a Leray-Hopf weak solution in $L^4 (0,T; L^4(Ω))$ for the incompressible Navier-Stokes system is persistence of energy due to Lions [19]. In this paper, it is shown that Lions's condition for energy balance is also valid for the weak solutions of the isentropic compressible Navier-Stokes equations allowing vacuum under suitable integrability conditions on the density and its derivative. This allows us to establish various sufficient conditions implying energy equality for the compressible flow as well as the non-homogenous incompressible Navier-Stokes equations. This is an improvement of corresponding results obtained by Yu in [32, Arch. Ration. Mech. Anal., 225 (2017)], and our criterion via the gradient of the velocity partially answers a question posed by Liang in [18, Proc. Roy. Soc. Edinburgh Sect. A (2020)].

math.AP↗
arXiv2021

Gagliardo-Nirenberg inequalities in Lorentz type spaces and energy equality for the Navier-Stokes system

In this paper, we derive some new Gagliardo-Nirenberg type inequalities in Lorentz type spaces without restrictions on the second index of Lorentz norms, which generalize almost all known corresponding results. Our proof mainly relies on the Bernstein inequalities in Lorentz spaces, the embedding relation among various Lorentz type spaces, and Littlewood-Paley decomposition techniques. In addition, we establish several novel criteria in terms of the velocity or the gradient of the velocity in Lorentz spaces for energy conservation of the 3D Navier-Stokes equations. Particularly, we improve the classical Shinbrot's condition for energy balance to allow both the space-time directions of the velocity to be in Lorentz spaces.

math.AP↗
arXiv2021

On non-resistive limit of 1D MHD equations with no vacuum at infinity

In this paper, we consider the Cauchy problem for the one-dimensional compressible isentropic magnetohydrodynamic (MHD) equations with no vacuum at infinity, but the initial vacuum can be permitted inside the region. By deriving a priori $ν$ (resistivity coefficient)-independent estimates, we establish the non-resistive limit of the global strong solutions with large initial data. Moreover, as a by-product, the global well-posedness of strong solutions for both the compressible resistive MHD equations and non-resistive MHD equations are also established, respectively.

math.AP↗
arXiv2019

On continuation criteria for the full compressible Navier-Stokes equations in Lorentz spaces

In this paper, we derive several new sufficient conditions of non-breakdown of strong solutions for for both the 3D heat-conducting compressible Navier-Stokes system and nonhomogeneous incompressible Navier-Stokes equations. First, it is shown that there exists a positive constant $\varepsilon$ such that the solution $(ρ,u,θ)$ to full compressible Navier-Stokes equations can be extended beyond $t=T$ provided that one of the following two conditions holds (1) $ρ\in L^{\infty}(0,T;L^{\infty}(\mathbb{R}^{3}))$, $u\in L^{p,\infty}(0,T;L^{q,\infty}(\mathbb{R}^{3}))$ and $$\| u\|_{L^{p,\infty}(0,T;L^{q,\infty}(\mathbb{R}^{3}))}\leq \varepsilon, ~~\text{with}~~ {2/p}+ {3/q}=1,\ \ q>3;$$ (2) $λ<3μ,$ $ρ\in L^{\infty}(0,T;L^{\infty}(\mathbb{R}^{3}))$, $θ\in L^{p,\infty}(0,T;L^{q,\infty}(\mathbb{R}^{3}))$ and $$\|θ\|_{L^{p,\infty}(0,T; L^{q,\infty}(\mathbb{R}^{3}))}\leq \varepsilon, ~~\text{with}~~ {2/p}+ {3/q}=2,\ \ q>3/2.$$ To the best of our knowledge, this is the first continuation theorem allowing the time direction to be in Lorentz spaces for the compressible fluid. Second, we establish some blow-up criteria in anisotropic Lebesgue spaces to the full Navier-Stokes system. Third, without the condition on $ρ$ in (0.1) and (0.3), the results also hold for the 3D nonhomogeneous incompressible Navier-Stokes equations. The appearance of vacuum in these systems could be allowed.

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