Jinlu Li
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View article: Ill-posedness in $B^s_{p,\infty}$ of the Euler equations: Non-continuous dependence
Ill-posedness in $B^s_{p,\infty}$ of the Euler equations: Non-continuous dependence Open
In this paper, we solve an open problem left in the monographs \cite[Bahouri-Chemin-Danchin, (2011)]{BCD}. Precisely speaking, it was obtained in \cite[Theorem 7.1 on pp293, (2011)]{BCD} the existence and uniqueness of $B^s_{p,\infty}$ sol…
View article: Comparative study on Organic Composts in Blueberry: Insights into Soil Physicochemical Properties and Heavy Metal Control
Comparative study on Organic Composts in Blueberry: Insights into Soil Physicochemical Properties and Heavy Metal Control Open
Organic fertilization is an essential method for sustainable agricultural development. Composts of edible fungal substrates (CEFS) and Chinese herbal residues (CCHR) are potential ecological organic fertilizers, but rarely used in blueberr…
View article: Ill-posedness and inviscid limit of basic equations of fluid dynamics in Besov spaces
Ill-posedness and inviscid limit of basic equations of fluid dynamics in Besov spaces Open
In this paper, we consider the Cauchy problem to the basic equations of fluid dynamics on the torus. Firstly, we construct a new initial data and provide a simple proof on the ill-posedness of $B^s_{p,\infty}$ solution of the Euler equatio…
View article: Covering constants for metric projection operator with applications to stochastic fixed-point problems
Covering constants for metric projection operator with applications to stochastic fixed-point problems Open
The theory of generalized differentiation in set-valued analysis is based on Mordukhovich derivative (Mordukhovich coderivative), which has been widely applied to optimization theory, equilibrium theory, variational analysis, with respect …
View article: Non-convergence of the Navier-Stokes equations toward the Euler equations in the endpoint Besov spaces
Non-convergence of the Navier-Stokes equations toward the Euler equations in the endpoint Besov spaces Open
In this paper, we consider the inviscid limit problem to the higher dimensional incompressible Navier-Stokes equations in the whole space. It was proved in \cite[J. Funct. Anal., 276 (2019)]{GZ} that given initial data $u_0\in B^{s}_{p,r}$…
View article: Continuity of Metric Projection Operator from C[0, 1] onto Pn with Applications to Mordukhovich Derivatives
Continuity of Metric Projection Operator from C[0, 1] onto Pn with Applications to Mordukhovich Derivatives Open
Let C[0, 1] be the Banach space of all continuous real valued functions on [0, 1]. For an arbitrarily given nonnegative integer n, let Pn denote the set of all polynomials with degree less than or equal to n. Pn is a closed subspace of C[0…
View article: Mordukhovich Derivatives of the Metric Projection Operator in Uniformly Convex and Uniformly Smooth Banach Spaces
Mordukhovich Derivatives of the Metric Projection Operator in Uniformly Convex and Uniformly Smooth Banach Spaces Open
In this paper, we investigate the properties of the Mordukhovich derivatives of the metric projection operator onto closed balls, closed and convex cylinders and positive cones in uniformly convex and uniformly smooth Banach spaces. We fin…
View article: Covering Constants for Metric Projection Operator with Applications to Stochastic Fixed-Point Problems
Covering Constants for Metric Projection Operator with Applications to Stochastic Fixed-Point Problems Open
In this paper, we use the Mordukhovich derivatives to precisely find the covering constants for the metric projection operator onto nonempty closed and convex subsets in uniformly convex and uniformly smooth Banach spaces. We consider thre…
View article: Mordukhovich derivatives of the normalized duality mapping in Banach spaces
Mordukhovich derivatives of the normalized duality mapping in Banach spaces Open
In this paper, we investigate some properties of the Mordukhovich derivatives of the normalized duality mapping in Banach spaces. For the underlying spaces, we consider three cases: uniformly convex and uniformly smooth Banach space lp; ge…
View article: Fixed-point properties of the Mordukhovich differential operator
Fixed-point properties of the Mordukhovich differential operator Open
In this paper, we investigate some fixed-point properties of the Mordukhovich differential operator of set valued mappings (or, single valued mappings) on Banach spaces. In particular, we study the fixed-point properties of the Mordukhovic…
View article: Dual and generalized dual cones in Banach spaces
Dual and generalized dual cones in Banach spaces Open
This paper proposes and analyzes the notion of dual cones associated with the metric projection and generalized projection in Banach spaces. We show that the dual cones, related to the metric projection and generalized metric projection, l…
View article: Global existence and blow-up for the Euler-Poincaré equations with a class of initial data
Global existence and blow-up for the Euler-Poincaré equations with a class of initial data Open
In this paper we investigate the Cauchy problem of d-dimensional Euler-Poincaré equations. By choosing a class of new and special initial data, we can transform this d-dimensional Euler-Poincaré equations into the Camassa-Holm type equatio…
View article: Well-posedness and no-uniform dependence for the Euler-Poincaré equations in Triebel-Lizorkin spaces
Well-posedness and no-uniform dependence for the Euler-Poincaré equations in Triebel-Lizorkin spaces Open
In this paper, we study the Cauchy problem of the Euler-Poincaré equations in $\R^d$ with initial data belonging to the Triebel-Lizorkin spaces. We prove the local-in-time unique existence of solutions to the Euler-Poincaré equations in $F…
View article: Ill-posedness issue on the Oldroyd-B model in the critical Besov spaces
Ill-posedness issue on the Oldroyd-B model in the critical Besov spaces Open
It is proved in \cite[J. Funct. Anal., 2020]{AP} that the Cauchy problem for some Oldroyd-B model is well-posed in $\B^{d/p-1}_{p,1}(\R^d) \times \B^{d/p}_{p,1}(\R^d)$ with $1\leq p<2d$. In this paper, we prove that the Cauchy problem for …
View article: Mordukhovich derivatives of the set-valued metric projection operator in general Banach spaces
Mordukhovich derivatives of the set-valued metric projection operator in general Banach spaces Open
In this paper, we investigate the properties and the precise solutions of the Mordukhovich derivatives of the set-valued metric projection operator onto some closed balls in some general Banach spaces. In the Banach space c, we find the pr…
View article: The failure of Hölder regularity of solutions for the Camassa--Holm type equation in Besov spaces
The failure of Hölder regularity of solutions for the Camassa--Holm type equation in Besov spaces Open
It is proved that if $u_0\in B^s_{p,r}$ with $s>1+\frac1p, (p,r)\in[1,+\infty]\times[1,+\infty)$ or $s=1+\frac1p, \ (p,r)\in[1,+\infty)\times \{1\}$, the solution of the Camassa--Holm equation belongs to $\mathcal{C}([0,T];B^s_{p,r})$. In …
View article: Mordukhovich derivatives of the metric projection operator in uniformly convex and uniformly smooth Banach spaces
Mordukhovich derivatives of the metric projection operator in uniformly convex and uniformly smooth Banach spaces Open
In this paper, we investigate the properties of the Mordukhovich derivatives of the metric projection operator onto closed balls, closed and convex cylinders and positive cones in uniformly convex and uniformly smooth Banach spaces. We fin…
View article: On the ill-posedness for the Navier--Stokes equations in the weakest Besov spaces
On the ill-posedness for the Navier--Stokes equations in the weakest Besov spaces Open
It is proved in \cite{IO21} that the Cauchy problem for the full compressible Navier--Stokes equations of the ideal gas is ill-posed in $\dot{B}_{p, q}^{2 / p}(\mathbb{R}^2) \times \dot{B}_{p, q}^{2 / p-1}(\mathbb{R}^2) \times \dot{B}_{p, …
View article: Frechet differentiability of the metric projection operator in Banach spaces
Frechet differentiability of the metric projection operator in Banach spaces Open
In this paper, we prove Frechet differentiability of the metric projection operator onto closed balls, closed and convex cylinders and positives cones in uniformly convex and uniformly smooth Banach spaces. With respect to these closed and…
View article: Generalized differentiability of the metric projection operator in Hilbert spaces
Generalized differentiability of the metric projection operator in Hilbert spaces Open
In this paper, we study the generalized differentiability of the metric projection operator in Hilbert spaces. We find exact expressions for Mordukhovich derivatives for the metric projection operator onto closed balls in Hilbert spaces an…
View article: Strict Frechet Differentiability of the Metric Projection Operator in Hilbert Spaces
Strict Frechet Differentiability of the Metric Projection Operator in Hilbert Spaces Open
In this paper, we prove strict Frechet differentiability of the metric projection operator onto closed balls in Hilbert spaces and onto positive cones in Euclidean spaces. We find the exact expressions for Frechet derivatives. Since Freche…
View article: Strict Frechet and generalized differentiability of the metric projection operator onto balls in Hilbert spaces
Strict Frechet and generalized differentiability of the metric projection operator onto balls in Hilbert spaces Open
In this paper, we prove strict Frechet differentiability of the metric projection operator onto closed balls in Hilbert spaces, and we find exact expressions for Frechet derivatives. Since Frechet differentiability implies Gateaux directio…
View article: OpenPerf: A Benchmarking Framework for the Sustainable Development of the Open-Source Ecosystem
OpenPerf: A Benchmarking Framework for the Sustainable Development of the Open-Source Ecosystem Open
Benchmarking involves designing scientific test methods, tools, and frameworks to quantitatively and comparably assess specific performance indicators of certain test subjects. With the development of artificial intelligence, AI benchmarki…
View article: Overseas Communication Strategy and Development Direction of Chinese Film and Television Works in the Internet Era
Overseas Communication Strategy and Development Direction of Chinese Film and Television Works in the Internet Era Open
In this paper, we first improve the influence propagation model by combining sentiment analysis and propose a new algorithm for node activation probability. Sentiment shift is the dynamic change of node attributes during the propagation of…
View article: Directional Differentiability of the Metric Projection in Bochner Spaces
Directional Differentiability of the Metric Projection in Bochner Spaces Open
In this paper, we consider the directional differentiability of metric projection and its properties in uniformly convex and uniformly smooth Bochner space Lp(S; X), in which (S, A, mu) is a positive measure space and X is a uniformly conv…
View article: Directional Differentiability of the Generalized Metric Projection in Banach Spaces
Directional Differentiability of the Generalized Metric Projection in Banach Spaces Open
Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X. In this paper, we consider the generalized metric projection operator from X to C, which was introduced by Alber in 1996. We…
View article: Directional Differentiability of the Generalized Metric Projection in Hilbert spaces and Hilbertian Bochner spaces
Directional Differentiability of the Generalized Metric Projection in Hilbert spaces and Hilbertian Bochner spaces Open
Let $H$ be a real Hilbert space and $C$ a nonempty closed and convex subset of $H$. Let $P_C: H\rightarrow C$ denote the (standard) metric projection operator. In this paper, we study the Gâteaux directional differentiability of $P_C$ and …
View article: Zero-filter limit issue for the Camassa-Holm equation in Besov spaces
Zero-filter limit issue for the Camassa-Holm equation in Besov spaces Open
In this paper, we focus on zero-filter limit problem for the Camassa-Holm equation in the more general Besov spaces. We prove that the solution of the Camassa-Holm equation converges strongly in $L^\infty(0,T;B^s_{2,r}(\R))$ to the invisci…
View article: Non-uniform convergence of solution for the Camassa-Holm equation in the zero-filter limit
Non-uniform convergence of solution for the Camassa-Holm equation in the zero-filter limit Open
In the short note, we prove that given initial data $\mathcal{u}_0 \in \pmb{H}^s(\mathbb{R})$ with $s>\frac32$ and for some $T>0$, the solution of the Camassa-Holm equation does not converges uniformly with respect to the initial data in $…