15 research outputs found
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 decay rate is
for any . By virtue of the time weighted energy
estimate, we can improve the decay rate to . 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
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
In this paper, we are concerned with optimal decay rate for the 2-D
generalized Oldroyd-B model with only stress tensor diffusion
. In the case , we first establish optimal
decay rate in 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 , 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
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 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 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 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