Related papers: Global strong solution to Maxwell-Dirac equations …
In this paper, we investigate Cauchy problem of the two-dimensional full Maxwell-Navier-Stokes system, and prove the global-in-time existence and uniqueness of solution in the borderline space which is very close to $L^2$-energy space by…
For vacuum Maxwell theory in four dimensions, a supplementary condition exists (due to Eastwood and Singer) which is invariant under conformal rescalings of the metric, in agreement with the conformal symmetry of the Maxwell equations.…
We prove the existence and exponential decay of global in time strong solutions to the Boltzmann equation without any angular cut-off, i.e., for long-range interactions. We consider perturbations of the Maxwellian equilibrium states and…
This paper focuses on the initial boundary value problem of two-dimensional non-resistive MHD equations in a half space. We prove that the MHD equations have a unique global strong solution around the equilibrium state $(0,\bf{e_1})$ for…
We find an exact solution to the Dirac equation in 1-1 dimensional space-time in the presence of a time-dependent potential which consists of a combination of electric, scalar, and pseudoscalar terms.
The global existence of weak solutions to the three space dimensional Prandtl equations is studied under some constraint on its structure. This is a continuation of our recent study on the local existence of classical solutions with the…
We obtain a class of rotating charged stationary circularly symmetric solutions of Einstein-Maxwell theory coupled to a topological mass term for the Maxwell field. These solutions are regular, have finite mass and angular momentum, and are…
We study the (2+1) dimensional Dirac equation in an homogeneous magnetic field (relativistic Landau problem) within a minimal length, or generalized uncertainty principle -GUP-, scenario. We derive exact solutions for a given explicit…
We construct a new class of solutions to the dispersionless hyper--CR equation, and show how any solution to this equation gives rise to a supersymmetric Einstein--Maxwell cosmological space--time in $(3+1)$--dimensions.
We quantize the massless p-form field that obeys the generalized Maxwell field equations in curved spacetimes of dimension n > 1. We begin by showing that the classical Cauchy problem of the generalized Maxwell field is well posed and that…
We prove the existence of a $L^2$-normalized solitary wave solution for the Maxwell-Dirac equations in (3+1)-Minkowski space. In addition, for the Coulomb-Dirac model, describing fermions with attractive Coulomb interactions in the…
It is known that the Maxwell-Klein-Gordon equations in $\mathbb{R}^{3+1}$ admit global solutions with finite energy data. In this paper, we present a new approach to study the asymptotic behavior of these global solutions. We show the…
Starting with the Dirac equation for an electron in a constant electromagnetic background on a noncommutative (NC) plane, we obtain a gauge invariant description of the system. Surprisingly, the dynamics of the system is dictated by the…
We apply the reduced radial gauge to give the general solution of the metric in 2+1 dimensions in term of quadratures. It allows a complete controll on the support of the source. We use the result to prove that for a general stationary…
On the (1+3) dimensional Minkowski spacetime, for small, regular initial data, it is well-known that the Dirac-Klein-Gordon system admits a global solution. In the present paper, we aim to establish the uniform boundedness of the total…
We obtain a new class of exact solutions for the Einstein-Maxwell system in static spherically symmetric charged star in (2+1)-dimensional gravity. In order to obtain the analytical solutions we treat the matter distribution anisotropic in…
A reduction of the Dirac-Maxwell equations in the case of static cylindrical symmetry is performed. The behaviour of the resulting system of o.d.e.'s is examined analytically and numerical solutions presented. There are two classes of…
The Maxwell-Klein-Gordon equations in 2+1 dimensions in temporal gauge are locally well-posed for low regularity data even below energy level. The corresponding (3+1)-dimensional case was considered by Yuan. Fundamental for the proof is a…
We consider the initial-boundary value problems on $\mathbb{R}^{+}\times \mathbb{R}^{+}$ for one-dimension systems of quasilinear wave equations with null conditions. We show that for homogeneous Dirichlet boundary values and sufficiently…
A combination of some weighted energy estimates is applied for the Cauchy problem of quasilinear wave equations with the standard null conditions in three spatial dimensions. Alternative proofs for global solutions are shown including the…