Related papers: Relatively non-degenerate integrated decay estimat…
We develop an existence, regularity and potential theory for nonlinear integrodifferential equations involving measure data. The nonlocal elliptic operators considered are possibly degenerate and cover the case of the fractional…
This paper aims to study the local behavior of solutions to a class of anisotropic weighted quasilinear degenerate parabolic equations with the weights comprising two power-type weights of different dimensions. We first capture the…
The collapse of a collisionless self-gravitating system, with the fast achievement of a quasi-stationary state, is driven by violent relaxation, with a typical particle interacting with the time-changing collective potential. It is…
We prove a large-data semi-global existence theorem and the dynamical formation of trapped surfaces for the Einstein-massless Vlasov system in 3+1 dimensions, without any symmetry assumptions. The analysis critically hinges on a finely…
We investigate cosmology-driven modifications to Schwarzschild-like black hole spacetimes and analyze their impact on photon propagation, gravitational lensing, and shadow observation. The gravitational deflection angle is computed using…
A new Morawetz or integrated local energy decay estimate for Maxwell test fields on the exterior of a Schwarzschild black hole spacetime is proved. The proof makes use of a new superenergy tensor $H_{ab}$ defined in terms of the Maxwell…
We present vacuum spacetime solutions of first order gravity, which are described by the exterior Schwarzschild geometry in one region and by degenerate tetrads in the other. The invertible and noninvertible phases of the tetrad meet at an…
We give a unified approach to weighted mixed-norm estimates and solvability for both the usual and time fractional parabolic equations in nondivergence form when coefficients are merely measurable in the time variable. In the spatial…
In this paper, we construct unique, local-in-time strong solutions to the Vlasov-Poisson (VP) and Vlasov-Poisson-Fokker-Planck (VPFP) systems subjected to external, spatially regular, white-in-time electromagnetic fields in $\mathbb T^d…
A multispecies, collisionless plasma is modeled by the Vlasov-Poisson system. Assuming the plasma is neutral and the electric field decays with sufficient rapidity as $t \to\infty$, we show that solutions can be constructed with arbitrarily…
The first article in a two-part series (the second article being [arXiv:2205.13197]) assumes a weak local energy decay estimate holds and proves that solutions to the linear wave equation with variable coefficients in $\mathbb R^{1+3}$,…
We show that a smooth, small enough Cauchy datum launches a unique classical solution of the relativistic Vlasov-Darwin (RVD) system globally in time. A similar result is claimed in Comm. Math. Sci. 6, 749-764 (2008) following the work in…
Weak gravitational lensing by black holes and wormholes in the context of massive gravity (Bebronne and Tinyakov 2009) theory is studied. The particular solution examined is characterized by two integration constants, the mass $M$ and an…
The Cauchy problem of the compressible Oldroyd-B model without damping mechanism in R^n$ with $n\ge2$ is considered. The lack of dissipation in density and stress tensor in the model is compensated by exploiting an intrinsic structure and…
We consider a 1D-2V Vlasov-Fokker-Planck multi-species ionic description coupled to fluid electrons. We address temporal stiffness with implicit time stepping, suitably preconditioned. To address temperature disparity in time and space, we…
Consider the Vlasov-Poisson-Landau system with Coulomb potential in the weakly collisional regime on a $3$-torus, i.e. $$\begin{aligned} \partial_t F(t,x,v) + v_i \partial_{x_i} F(t,x,v) + E_i(t,x) \partial_{v_i} F(t,x,v) = \nu…
We prove local energy decay for the damped wave equation on R^d. The problem which we consider is given by a long range metric perturbation of the Euclidean Laplacian with a short range absorption index. Under a geometric control assumption…
This article is devoted to the study of new exact analytical solutions in the background of Reissner-Nordstr\"{o}m space-time by using gravitational decoupling via minimal geometric deformation approach. To do so, we impose the most general…
We examine linear perturbation theory to evaluate the contribution of viscosity coefficient in the growing of dark matter perturbations in the context of the bulk viscous dark energy model inspired by thermodynamical dissipative phenomena…
In this work, we consider the smoothing effect of Vlasov-Poisson-Landau system for both hard and soft potential. In particular, we prove that any classical solutions becomes immediately smooth with respect to all variables. We also give a…