Related papers: Decoupled energy estimates for tensorial non-linea…
This work concerns a general system of energy-critical wave equations in the Minkowski space of dimension $1+3$. The wave equations are coupled by the nonlinearities, which are homogeneous of degree 5. We prove that any radial solution of…
We prove a conformally invariant estimate for the index of Schr\"odinger operators acting on vector bundles over four-manifolds, related to the classical Cwikel-Lieb-Rozenblum estimate. Applied to Yang-Mills connections we obtain a bound…
The well known relation of Einstein relativistic energy for a free particle is extended to cover the total relativistic energy of a bound particle by calculating the relativistic potential energy. A non dissipative harmonic oscillator…
We show that a connection can be recovered up to gauge from source-to-solution type data associated with the Yang-Mills equations in the four dimensional Minkowski space. Our proof analyzes the principal symbols of waves generated by…
This work proposes a suite of numerical techniques to facilitate the design of structure-preserving integrators for nonlinear dynamics. The celebrated LaBudde-Greenspan integrator and various energy-momentum schemes adopt a difference…
We consider the problem of ''energy conserving'' lattice Boltzmann models. A major difficulty observed in previous studies is the coupling between the viscous and thermal waves even at moderate wave numbers. We propose a theoretical…
The Maxwell theory on non-commutative spaces has been considered. The non-linear equations of electromagnetic fields on non-commutative spaces were obtained in the compact spin-tensor (quaternion) form. It was shown that the plane…
This work first gives the global existence and optimal decay rates of solutions to the classical Timoshenko system on the framework of Besov spaces. Due to the \textit{non-symmetric} dissipation, the general theory for dissipative…
We propose a novel tensor network representation for two-dimensional Yang-Mills theories with arbitrary compact gauge groups. In this method, tensor indices are directly given by group elements with no direct use of the character expansion.…
We present a new method for the analysis of electromagnetic scattering from homogeneous penetrable bodies. Our approach is based on a reformulation of the governing Maxwell equations in terms of two uncoupled vector Helmholtz systems: one…
We consider gauge theories on Poisson manifolds emerging as semiclassical approximations of noncommutative spacetime with Lie algebra type noncommutativity. We prove an important identity, which allows to obtain simple and manifestly…
We propose a numerical integrator for the coupled system of the eddy-current equation with the nonlinear Landau-Lifshitz-Gilbert equation. The considered effective field contains a general field contribution, and we particularly cover…
In this paper, we develop a novel class of linear energy-preserving integrating factor methods for the 2D nonlinear Schr\"odinger equation with wave operator (NLSW), combining the scalar auxiliary variable approach and the integrating…
The canonical energy-momentum tensor is often considered as a purely academic object because of its gauge dependence. However, it has recently been realized that canonical quantities can in fact be defined in a gauge-invariant way provided…
We give a short proof of the existence of a small piece of null infinity for $(3+1)$-dimensional spacetimes evolving from asymptotically flat initial data as solutions of the Einstein vacuum equations. We introduce a modification of the…
This paper extends the research on the self-consistent effective-one-body theory of a real spinless two-body system based on the post-Minkowskian approximation (Science China, 65, 100411, (2022)) to the case of a binary system for the…
We derive a formalism for solving the Lorenz gauge equations for metric perturbations of Kerr spacetime sourced by an arbitrary stress-energy tensor. The metric perturbation is obtained as a sum of differential operators acting on a set of…
Future developments of lighter, more compact and powerful motors-driven by environmental and sustainability considerations in the transportation industry-involve higher stresses, currents and electromagnetic fields. Strong couplings between…
We establish local energy decay for damped magnetic wave equations on stationary, asymptotically flat space-times subject to the geometric control condition. More specifically, we allow for the addition of time-independent magnetic and…
In this paper we pay attention to the inconsistency in the derivation of the symmetric electromagnetic energy-momentum tensor for a system of charged particles from its canonical form, when the homogeneous Maxwell equations are applied to…