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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Normalized solutions of nonlinear Schrodinger equations with exponential critical growth
指数临界增长 非线性薛定谔方程 归一化解
2023/5/15
In this talk, we consider normalized solutions of nonlinear Schrodinger equations in the plane when the nonlinearity satisfies an exponential critical growth. To study the normalized solutions by usin...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Global unique solutions for the inhomogeneous Navier-Stokes equation with only bounded density, in critical regularity spaces
临界正则性空间 界密度 非齐次 纳维-斯托克斯方程 全局唯一解
2023/4/25
Our work is to prove the global existence and uniqueness of solutions to the inhomogeneous incompressible Navier-Stokes system in the case where the initial density $\rho_0$ is discontinuous and the i...
On solutions of Maxwell’s equations with dipole sources over a thin conducting film
solutions of Maxwell’s equations dipole sources conducting film
2015/10/16
We derive and interpret solutions of time-harmonic Maxwell’s equations with a vertical and a horizontal electric dipole near a planar, thin conducting film, e.g. Graphene sheet, lying between two unbo...
Cosmological multi-black-hole solutions
Einstein Maxwell equation the charged black holes time and space actively the cosmological constant a black hole
2014/12/23
We present simple, analytic solutions to the Einstein-Maxwell equation, which describe an arbitrary number of charged black holes in a spacetime with a positive cosmological constant Λ. In the limit Λ...
Supersymmetry and stationary solutions in dilaton-axion gravity
Gravity is fixed charged Taub - the NUT steel pipe concrete the construction
2014/12/23
New stationary solutions of four-dimensional dilaton-axion gravity are presented, which correspond to the charged Taub-NUT and Israel-Wilson-Perjés (IWP) solutions of Einstein-Maxwell theory. The char...
A Family of Exact, Analytic Time Dependent Wave Packet Solutions to a Nonlinear Schroedinger Equation
A Family of Exact Analytic Time Dependent Packet Solutions Nonlinear Schroedinger Equation Mathematical Physics
2012/6/19
We obtain time dependent $q$-Gaussian wave-packet solutions to a non linear Schr\"odinger equation recently advanced by Nobre, Rego-Montero and Tsallis (NRT) [Phys. Rev. Lett. 106 (2011) 10601]. The N...
Relativistic point dynamics and Einstein formula as a property of localized solutions of a nonlinear Klein-Gordon equation
Relativistic point dynamics Einstein formula nonlinear Klein-Gordon equation Mathematical Physics
2012/6/15
Einstein's relation E=Mc^2 between the energy E and the mass M is the cornerstone of the relativity theory. This relation is often derived in a context of the relativistic theory for closed systems wh...
Exact Analytic Solutions for the Rotation of an Axially Symmetric Rigid Body Subjected to a Constant Torque
Exact Analytic Solutions Rotation Axially Symmetric Rigid Body Constant Torque
2012/4/24
New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. ...
Special solutions to a compact equation for deep-water gravity waves
Special solutions compact equation deep-water gravity waves Classical Physics
2012/4/24
Recently, Dyachenko & Zakharov (2011) have derived a compact form of the well known Zakharov integro-differential equation for the third order Hamiltonian dynamics of a potential flow of an incompress...
Alternate powers in Serrin's swirling vortex solutions
Serrin’s swirling vortex Navier–Stokes equations Euler equations Cai’s power law tornado modeling vortex breakdown
2012/4/23
We consider a modification of the fluid flow model for a swirling vortex developed by J. Serrin, where velocity decreases as the reciprocal of the distance from the vortex axis. Recent studies, based ...
Constant curvature solutions of Grassmannian sigma models: (1) Holomorphic solutions
Sigma models Mathematical Physics Holomorphic solutions
2012/4/18
We present a general formula for the Gaussian curvature of curved holomorphic 2-spheres in Grassmannian manifolds G(m, n). We then show how to construct such solutions with constant curvature. We also...
Exact polynomial solutions of second order differential equations and their applications
Polynomial solutions Bethe ansatz Quasi-exactly solvable systems
2011/9/21
Abstract: We find all polynomials $Z(z)$ such that the differential equation $${X(z)\frac{d^2}{dz^2}+Y(z)\frac{d}{dz}+Z(z)}S(z)=0,$$ where $X(z), Y(z), Z(z)$ are polynomials of degree at most 4, 3, 2 ...
Uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system
Vlasov-Darwin weak solutions uniqueness optimal transportation
2011/9/20
Abstract: We use optimal transportation techniques to show uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system. Our proof extends the method used by Loeper in...
Global Classical and Weak Solutions to the Three-Dimensional Full Compressible Navier-Stokes System with Vacuum and Large Oscillations
Global Classical Weak Solutions Three-Dimensional Full Compressible Navier-Stokes System Vacuum and Large Oscillations
2011/9/19
Abstract: We establish the global existence and uniqueness of classical solutions to the three-dimensional full compressible Navier-Stokes system with smooth initial data which are of small energy but...
State-space solutions to the dynamic magnetoencephalography inverse problem using high performance computing
Magnetoencephalography source localization Kalman filter fixed interval smoother
2011/8/17
Abstract: Determining the magnitude and location of neural sources within the brain that are responsible for generating magnetoencephalography (MEG) signals measured on the surface of the head is a ch...