This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the n...This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.展开更多
In this paper,we investigate the dynamical stability of transonic shock solutions for the full compressible Euler system in a two dimensional nozzle with a symmetric divergent part.Building upon the existence and uniq...In this paper,we investigate the dynamical stability of transonic shock solutions for the full compressible Euler system in a two dimensional nozzle with a symmetric divergent part.Building upon the existence and uniqueness results for steady symmetric transonic shock solutions to the nonisentropic Euler system established in[Z.P.Xin and H.C.Yin,The transonic shock in a nozzle,2-D and 3-D complete Euler systems,J.Differential Equations 245(2008)],we prove the dynamical stability of the transonic shock solutions under small perturbations.More precisely,if the initial unsteady transonic flow is located in the symmetric divergent part of the nozzle and the flow is a symmetric small perturbation of the steady transonic flow,we use the characteristic method to establish the dynamical stability.展开更多
The topological phases and edge states of a topological Euler insulator on a triangular lattice is studied.Differently from two-band Chern insulators,a topological Euler insulator is a kind of three-band model,describ...The topological phases and edge states of a topological Euler insulator on a triangular lattice is studied.Differently from two-band Chern insulators,a topological Euler insulator is a kind of three-band model,described by the Euler number not the Chern number.The spin textures of a topological Euler insulator in the momentum space is like a Néel-type skyrmion.It is found that the topological edge states exist in the band gap of the topological Euler insulator,and the topological Euler insulator can be transformed into a topological metal without the topological phase transition.展开更多
In this paper,we consider the inhomogeneous pressureless Euler equations.First,we present a class of self-similar analytical solutions to the 1D Cauchy problem and investigate the large-time behavior of the solutions,...In this paper,we consider the inhomogeneous pressureless Euler equations.First,we present a class of self-similar analytical solutions to the 1D Cauchy problem and investigate the large-time behavior of the solutions,and particularly,we obtain slant kink-wave solutions for the inhomogeneous Burgers(InhB)type equation.Next,we prove the integrability of the InhB equation in the sense of Lax pair.Furthermore,we study the spreading rate of the moving domain occupied by mass for the 1D Cauchy problem with compact support initial density.We find that the expanding domain grows exponentially in time,provided that the solutions exist and smooth at all time.Finally,we extend the corresponding results of the inhomogeneous pressureless Euler equations to the radially symmetric multi-dimensional case.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12471394,12371417)Natural Science Foundation of Changsha(No.kq2502101)。
文摘This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.
基金supported in part by NSFC(Grant Nos.12271205,12171498).
文摘In this paper,we investigate the dynamical stability of transonic shock solutions for the full compressible Euler system in a two dimensional nozzle with a symmetric divergent part.Building upon the existence and uniqueness results for steady symmetric transonic shock solutions to the nonisentropic Euler system established in[Z.P.Xin and H.C.Yin,The transonic shock in a nozzle,2-D and 3-D complete Euler systems,J.Differential Equations 245(2008)],we prove the dynamical stability of the transonic shock solutions under small perturbations.More precisely,if the initial unsteady transonic flow is located in the symmetric divergent part of the nozzle and the flow is a symmetric small perturbation of the steady transonic flow,we use the characteristic method to establish the dynamical stability.
基金supported by the National Natural Science Foundation of China(Grants Nos.12174288 and 12274326)the National Key R&D Program of China(Grant No.2021YFA1400602)。
文摘The topological phases and edge states of a topological Euler insulator on a triangular lattice is studied.Differently from two-band Chern insulators,a topological Euler insulator is a kind of three-band model,described by the Euler number not the Chern number.The spin textures of a topological Euler insulator in the momentum space is like a Néel-type skyrmion.It is found that the topological edge states exist in the band gap of the topological Euler insulator,and the topological Euler insulator can be transformed into a topological metal without the topological phase transition.
基金Supported by the Henan Natural Science Foundation(242300421397)the Basic Research Projects of Key Scientific Research Projects Plan in Henan Higher Education Institutions(25ZX013)+2 种基金the Scientific Research Team Plan of Zhengzhou University of Aeronautics(23ZHTD01003)the National Natural Science Foundation of China(11971475)the FLASS Internationalization and Exchange Scheme(FLASS/IE−D09/19-20−FLASS).
文摘In this paper,we consider the inhomogeneous pressureless Euler equations.First,we present a class of self-similar analytical solutions to the 1D Cauchy problem and investigate the large-time behavior of the solutions,and particularly,we obtain slant kink-wave solutions for the inhomogeneous Burgers(InhB)type equation.Next,we prove the integrability of the InhB equation in the sense of Lax pair.Furthermore,we study the spreading rate of the moving domain occupied by mass for the 1D Cauchy problem with compact support initial density.We find that the expanding domain grows exponentially in time,provided that the solutions exist and smooth at all time.Finally,we extend the corresponding results of the inhomogeneous pressureless Euler equations to the radially symmetric multi-dimensional case.
