In this paper,we study the ground state standing wave solutions for the focusing bi-harmonic nonlinear Schrodinger equation with aμ-Laplacian term(BNLS).Such BNLS models the propagation of intense laser beams in a bu...In this paper,we study the ground state standing wave solutions for the focusing bi-harmonic nonlinear Schrodinger equation with aμ-Laplacian term(BNLS).Such BNLS models the propagation of intense laser beams in a bulk medium with a second-order dispersion term.Denoting by Qpthe ground state for the BNLS withμ=0,we prove that in the mass-subcritical regime p∈(1,1+8/d),there exist orbit ally stable ground state solutions for the BNLS when p∈(-λ0,∞)for someλ0=λ0(p,d,‖Qp‖L2)>0.Moreover,in the mass-critical case p=1+8/d,we prove the orbital stability on a certain mass level below‖Q*‖L2,provided thatμ∈(-λ1,0),where■and Q*=Q1+8/d.The proofs are mainly based on the profile decomposition and a sharp Gagliardo-Nirenberg type inequality.Our treatment allows us to fill the gap concerning the existence of the ground states for the BNLS when p is negative and p∈(1,1+8/d].展开更多
Let H be a Schroedinger operator on R^n. Under a polynomial decay condition for the kernel of its spectral operator, we show that the Besov spaces and Triebel-Lizorkin spaces associated with H are well defined. We fur...Let H be a Schroedinger operator on R^n. Under a polynomial decay condition for the kernel of its spectral operator, we show that the Besov spaces and Triebel-Lizorkin spaces associated with H are well defined. We further give a Littlewood-Paley characterization of Lp spaces in terms of dyadic functions of H. This generalizes and strengthens the previous result when the heat kernel of H satisfies certain upper Gaussian bound.展开更多
We obtain certain time decay and regularity estimates for 3D Schroedinger equation with a potential in the Kato class by using Besov spaces associated with Schroedinger operators.
We prove a complex and a real interpolation theorems on Besov spaces and Triebel-Lizorkin spaces associated with a selfadjoint operator L, without assuming the gradient estimate for its spectral kernel. The result app...We prove a complex and a real interpolation theorems on Besov spaces and Triebel-Lizorkin spaces associated with a selfadjoint operator L, without assuming the gradient estimate for its spectral kernel. The result applies to the cases where L is a uniformly elliptic operator or a Schrdinger operator with electro-magnetic potential.展开更多
基金partially supported by the National Natural Science Foundation of China(11501137)partially supported by the National Natural Science Foundation of China(11501395,12071323)the Guangdong Basic and Applied Basic Research Foundation(2016A030310258,2020A1515011019)。
文摘In this paper,we study the ground state standing wave solutions for the focusing bi-harmonic nonlinear Schrodinger equation with aμ-Laplacian term(BNLS).Such BNLS models the propagation of intense laser beams in a bulk medium with a second-order dispersion term.Denoting by Qpthe ground state for the BNLS withμ=0,we prove that in the mass-subcritical regime p∈(1,1+8/d),there exist orbit ally stable ground state solutions for the BNLS when p∈(-λ0,∞)for someλ0=λ0(p,d,‖Qp‖L2)>0.Moreover,in the mass-critical case p=1+8/d,we prove the orbital stability on a certain mass level below‖Q*‖L2,provided thatμ∈(-λ1,0),where■and Q*=Q1+8/d.The proofs are mainly based on the profile decomposition and a sharp Gagliardo-Nirenberg type inequality.Our treatment allows us to fill the gap concerning the existence of the ground states for the BNLS when p is negative and p∈(1,1+8/d].
文摘Let H be a Schroedinger operator on R^n. Under a polynomial decay condition for the kernel of its spectral operator, we show that the Besov spaces and Triebel-Lizorkin spaces associated with H are well defined. We further give a Littlewood-Paley characterization of Lp spaces in terms of dyadic functions of H. This generalizes and strengthens the previous result when the heat kernel of H satisfies certain upper Gaussian bound.
文摘We obtain certain time decay and regularity estimates for 3D Schroedinger equation with a potential in the Kato class by using Besov spaces associated with Schroedinger operators.
文摘We prove a complex and a real interpolation theorems on Besov spaces and Triebel-Lizorkin spaces associated with a selfadjoint operator L, without assuming the gradient estimate for its spectral kernel. The result applies to the cases where L is a uniformly elliptic operator or a Schrdinger operator with electro-magnetic potential.
基金the National Natural Science Foundation of China(Grant Nos.11427904,12025506,and 12172357)the Key Scientific Instruments Development Program of CAS(Grant No.GJJSTD20210007)the Key Projects of Guangdong Basic and Applied Basic Research Fund Joint Fund(Grant No.2022B1515120051).
文摘中国科学院近代物理研究所正在研发第四代ECR(电子回旋共振)离子源FECR(first 4th generation ECR ion source).以20 kW/45 GHz微波加热运行为目标,需要研制Nb_(3)Sn超导磁体以实现对所加热等离子体的有效磁场约束.作为首台采用Nb_(3)Sn超导磁体技术的ECR离子源,FECR的主磁场线圈由4套独立的轴向螺线管线圈与1套径向六极线圈所构成,且均采用单股Nb_(3)Sn线绕制而成,这给线圈的加工、冷体装配、磁体的失超保护等环节带来一系列挑战.为使磁体能在高场、高应力作用下安全稳定运行,项目采用基于铝壳体结构与bladder&key的预紧应力控制技术,完成了一套半尺寸冷体样机的研发.该样机已完成4.2 K低温测试.本项研究的核心关键问题与挑战是如何在复杂的高精度机械装配与高电流强磁场励磁过程中实现对易碎Nb_(3)Sn导线的有效保护.本篇文章中,我们将阐述如何设计、研制、装配及测试工作于复杂磁场与应力环境的高性能Nb_(3)Sn六极磁铁.针对于单个六极线圈的测试,我们设计研发了一种称为“Mirror”结构的测试工装.论文中会详细论述基于壳层结构与bladder&key的装配预紧技术在半尺寸样机上的应用效果.同时,论文对在半尺寸样机上观察到的强烈磁通跳跃现象和它对失超探测保护的严峻挑战问题及相关解决或规避方案进行相关论述.
