Large time behavior of global strong solutions to the 2-D compressible FENE dumbbell model

In this paper, we mainly study large time behavior of the strong solutions to the 2-D compressible finite extensible nonlinear elastic (FENE) dumbbell model. The Fourier splitting method yields that the $L^2$ decay rate is $\ln^{-l}(e+t)$ for any $l\in\mathbb{N}$. By virtue of the time weighted energy estimate, we can improve the decay rate to $(1+t)^{-\frac{1}{4}}$. Under the low-frequency condition and by the Littlewood-Paley theory, we show that the solutions belong to some Besov space with negative index and obtain the optimal $L^2$ decay rate.Comment: 22 pages. arXiv admin note: substantial text overlap with arXiv:2107.0864

Optimal decay rate for the generalized Oldroyd-B model with only stress tensor diffusion in R2\mathbb{R}^2

In this paper, we are concerned with optimal decay rate for the 2-D generalized Oldroyd-B model with only stress tensor diffusion $(-\Delta)^{\beta}\tau$. In the case $\beta=1$, we first establish optimal decay rate in $H^1$ framework and remove the smallness assumption of low frequencies by virtue of the Fourier splitting method and the Littlewood-Paley decomposition theory. Furthermore, we prove optimal decay rate for the highest derivative of the solution by a different method combining time frequency decomposition and the time weighted energy estimate. In the case $\frac 1 2\leq \beta <1$, we study optimal decay rate for the highest derivative of the solution by the improved Fourier splitting method.Comment: 24 pages. arXiv admin note: text overlap with arXiv:2110.1233

Globally conservative solutions for the modified Camassa–Holm (MOCH) equation

In this paper, we present the globally conservative solutions to the Cauchy problem for the modified Camassa–Holm (MOCH) equation. First, we transform the equation into an equivalent semi-linear system under new variables. Second, according to the standard ordinary differential equation theory with the aid of the conservation law, we give the global solutions of the semi-linear system. Finally, returning to the original variables, we obtain the globally conservative solutions to the MOCH equation

Global solutions and large time behavior for some Oldroyd-B type models in R2R^2

In this paper, we are concerned with global solutions to the co-rotation Oldroyd-B type model and large time behavior for the general Oldroyd-B type model. We first establish the energy estimate and B-K-M criterion for the 2-D co-rotation Oldroyd-B type model. Then, we obtain global solutions by proving the boundedness of vorticity. In general case, we apply Fourier spiltting method to prove the $H^1$ decay rate for global solutions constructed by T.M.Elgindi and F.Rousset

Global existence and optimal decay rate of weak solutions to some inviscid Oldroyd-B models

This paper is devoted to global existence and optimal decay rate of weak solutions to some inviscid Oldroyd-B models with center diffusion. By virtue of the properties of Calderon-Zygmund operator and the Littlewood-Paley decomposition theory, we firstly prove that the 2-D co-rotation inviscid Oldroyd-B model admits global weak solutions with some large data under different integrability conditions. Furthermore, we prove the energy conservation of weak solutions for the co-rotation case. These obtained results generalize and cover the classical results for the Euler equation. Moreover, we establish global weak solutions with small data for the 2-D noncorotation inviscid Oldroyd-B model without damping. Finally, we prove optimal decay rate of global weak solutions for the noncorotation case by the improved Fourier splitting method.Comment: 44 page

Global existence and optimal decay rate of weak solutions to the co-rotation Hooke dumbbell model

In this paper, we mainly study global existence and optimal $L^2$ decay rate of weak solutions to the co-rotation Hooke dumbbell model. This micro-macro model is a coupling of the Navier-Stokes equation with a nonlinear Fokker-Planck equation. Based on the defect measure propagation method, we prove that the co-rotation Hooke dumbbell model admits a global weak solution provided the initial data under different integrability conditions. Moreover, we obtain optimal long time decay rate in $L^2$ for the weak solutions obtained by the Fourier splitting method

Public-key Cryptosystems and Signature Schemes from p-adic Lattices

In 2018, the longest vector problem and closest vector problem in local fields were introduced, as the p-adic analogues of the shortest vector problem and closest vector problem in lattices of Euclidean spaces. They are considered to be hard and useful in constructing cryptographic primitives, but no applications in cryptography were given. In this paper, we construct the first signature scheme and public-key encryption cryptosystem based on p-adic lattice by proposing a trapdoor function with the orthogonal basis of p-adic lattice. These cryptographic schemes have reasonable key size and efficiency, which shows that p-adic lattice can be a new alternative to construct cryptographic primitives and well worth studying

Tighter monogamy and polygamy relations in multiqubit systems

In this paper, we investigate some monogamy and polygamy relations in terms of concurrence, Rényi α-entropy entanglement and Tsallis q-entropy entanglement. Those relations are tighter than the existing monogamy and polygamy relations. As application, we give some examples in detail