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This article proposes authentication and physical layer security schemes to improve secure communications between the electric vehicle (EV) and charging infrastructure in dynamic wireless power transfer (DWPT) systems. In particular, a double-encryption with the signature (DoES) scheme is proposed for session key exchange between EV and charging station which provides data authenticity and integrity. To enable low-latency authentication between EV and power transmitter (PT) in DWPT systems, a sign-encrypt-message (SEM) authentication code scheme is designed leveraging symmetric keys for dynamic charging, which ensures privacy and resistance to tampering attacks. The artificial noise-based physical layer security (AN-based PLS) scheme is also proposed at the physical layer to degrade the wiretapped signal quality of multiple eavesdroppers operating in non-colluding and colluding cases. Closed-form expressions for the secrecy outage probability (SOP) and intercept probability (IP) of the considered system with the non-colluding case are derived to show that the proposed AN-based PLS scheme provides lower SOP and IP than the conventional ones without AN. The distance between eavesdroppers and the PT also affects the system SOP and IP in both non-colluding and colluding cases. Moreover, the EV using the DoES scheme takes 52 ms for obtaining session keys from the charging station while it only spends 8.23 ms with the SEM scheme to authenticate with PT for the charging process. 

This paper is the continuation of a program, initiated in Grenier and Nguyen [SIAM J.Math. Anal. 51 (2019); J. Differential Equations 269 (2020)], to derive pointwise estimates on theGreen function of Orr–Sommerfeld equations. In this paper we focus on long wavelength perturbations, more precisely horizontal wave numbers\alphaof order\nu^{1/4}, which correspond to the lower boundary of the instability area for monotonic profiles.

 

Consider the Vlasov–Poisson–Landau system with Coulomb potential in the weakly collisional regime on a$3$-torus, i.e.$\begin{align*} \partial _t F(t,x,v) + v_i \partial _{x_i} F(t,x,v) + E_i(t,x) \partial _{v_i} F(t,x,v) = \nu Q(F,F)(t,x,v),\\ E(t,x) = \nabla \Delta ^{-1} (\int _{\mathbb R^3} F(t,x,v)\, \mathrm {d} v - {{\int }\llap {-}}_{\mathbb T^3} \int _{\mathbb R^3} F(t,x,v)\, \mathrm {d} v \, \mathrm {d} x), \end{align*}$with$\nu \ll 1$. We prove that for$\epsilon >0$sufficiently small (but independent of$\nu$), initial data which are$O(\epsilon \nu ^{1/3})$-Sobolev space perturbations from the global Maxwellians lead to global-in-time solutions which converge to the global Maxwellians as$t\to \infty$. The solutions exhibit uniform-in-$\nu$Landau damping and enhanced dissipation.

Our main result is analogous to an earlier result of Bedrossian for the Vlasov–Poisson–Fokker–Planck equation with the same threshold. However, unlike in the Fokker–Planck case, the linear operator cannot be inverted explicitly due to the complexity of the Landau collision operator. For this reason, we develop an energy-based framework, which combines Guo’s weighted energy method with the hypocoercive energy method and the commuting vector field method. The proof also relies on pointwise resolvent estimates for the linearized density equation.

 

We prove the inviscid limit for the incompressible Navier-Stokes equations for data that are analytic only near the boundary in a general two-dimensional bounded domain. Our proof is direct, using the vorticity formulation with a nonlocal boundary condition, the explicit semigroup of the linear Stokes problem near the flatten boundary, and the standard wellposedness theory of Navier-Stokes equations in Sobolev spaces away from the boundary.