Related papers: Localized continuation criterion, improved local e…
Global properties of maximal future Cauchy developments of stationary, m-dimensional asymptotically flat initial data with an outer trapped boundary are analyzed. We prove that, whenever the matter model is well posed and satisfies the null…
The goal of this work is to study a model of the wave equation with dynamic boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin method combined with the fixed point theorem, we show the existence and uniqueness…
Given a parameter dependent fixed point equation $x = F(x,u)$, we derive an abstract compactness principle for the fixed point map $u \mapsto x^*(u)$ under the assumptions that (i) the fixed point equation can be solved by the contraction…
In this article we initiate a systematic study of the well-posedness theory of the Einstein constraint equations on compact manifolds with boundary. This is an important problem in general relativity, and it is particularly important in…
We investigate the blowup criterion of the barotropic compressible viscous fluids for the Cauchy problem, Dirichlet problem and Navier-slip boundary condition. The main novelty of this paper is two-fold: First, for the Cauchy problem and…
In this paper, vacuum and singularity formation are considered for compressible Euler equations with time-dependent damping. For $1<\gamma\leq 3$, by constructing some new control functions ingeniously, we obtain the lower bounds estimates…
The main objective of this paper is a study of the asymptotic behavior of distributional solutions to the one-dimensional repulsive pressureless Euler-Poisson system. The system is a model for the dynamics of a mass distribution evolving on…
This talk describes some recent results [16] regarding the problem of uniqueness in the large (also known as strong cosmic censorship) for the initial value problem in general relativity. In order to isolate the essential analytic features…
We study McKean-Vlasov equations where the coefficients are locally Lipschitz continuous. We prove the strong well-posedness and a propagation of chaos property in this framework. These questions can be treated with classical arguments…
In this article, we study Lions' density patch problem in two space dimensions at critical regularity. We prove global existence, uniqueness, and stability for a fluid occupying a bounded Lipschitz region surrounded by vacuum and evolving…
We consider the Cauchy problem for the Gross-Pitaevskii infinite linear hierarchy of equations on $\mathbb{R}^n.$ By introducing a (F)-norm in certain Sobolev type spaces of sequences of marginal density matrices, we establish local…
In this paper, we consider the Kawahara equation in a bounded interval and with a delay term in one of the boundary conditions. Using two different approaches, we prove that this system is exponentially stable under a condition on the…
We study the mathematical theory of second order systems with two species, arising in the dynamics of interacting particles subject to linear damping, to nonlocal forces and to external ones, and resulting into a nonlocal version of the…
Here we consider the nonlocal Cahn-Hilliard equation with constant mobility in a bounded domain. We prove that the associated dynamical system has an exponential attractor, provided that the potential is regular. In order to do that a…
We are concerned with the existence and uniqueness of solutions with only bounded density for the barotropic compressible Navier-Stokes equations. Assuming that the initial velocity has slightly sub-critical regularity and that the initial…
The asymptotic behaviour of vacuum Bianchi models of class A near the initial singularity is studied, in an effort to confirm the standard picture arising from heuristic and numerical approaches by mathematical proofs. It is shown that for…
We address the compressible magnetohydrodynamics (MHD) equations in $\mathbb{R}^3$ and establish a blow-up criterion for the local strong solutions in terms of the density only. Namely, if the density is away from vacuum ($\rho= 0$) and the…
In this paper, we extend some results of nonsmooth analysis from Euclidean context to the Riemannian setting. In particular, we discuss the concept and some properties of locally Lipschitz continuous vector fields on Riemannian settings,…
In this paper, we continue the analysis of the stationary exterior Navier-Stokes problem with interior boundary data and vanishing condition at infinity. We first show an existence result that extends a previous contribution of the second…
We study closure properties of measurable ultrapowers with respect to Hamkin's notion of "freshness" and show that the extent of these properties highly depends on the combinatorial properties of the underlying model of set theory. In one…