Related papers: Global well-posedness for the nonlinear generalize…
The goal of this paper is to establish a global well-posedness for a broad class of strictly hyperbolic Cauchy problems with coefficients in $C^2((0,T];C^\infty(\mathbb{R}^n))$ growing polynomially in $x$ and singular in $t$. The problems…
We prove a local in time existence and uniqueness theorem of classical solutions of the coupled Einstein--Euler system, and therefore establish the well posedness of this system. We use the condition that the energy density might vanish or…
We prove the global well-posedness of the so-called hyperbolic relaxation of the Cahn-Hilliard-Oono equation in the whole space R^3 with the non-linearity of the sub-quintic growth rate. Moreover, the dissipativity and the existence of a…
We consider an evolution equation inspired by a model in peridynamics, with a singular pairwise interaction force term, and we give global in time existence, uniqueness and stability results for the Cauchy problem.
We study a one-dimensional nonlinear hyperbolic-parabolic initial boundary value problem occurring in the theory of thermoelasticity. We prove existence and uniqueness of the local-in-time strong solution. Also, some global-in-time weak…
We prove almost global well-posedness for quasilinear strongly coupled wave-Klein-Gordon systems with small and localized data in two space dimensions. We assume only mild decay on the data at infinity as well as minimal regularity. We…
We show global wellposedness for the defocusing cubic nonlinear Schr\"odinger equation (NLS) in $H^1(\mathbb{R}) + H^{3/2+}(\mathbb{T})$, and for the defocusing NLS with polynomial nonlinearities in $H^1(\mathbb{R}) + H^{5/2+}(\mathbb{T})$.…
The Anderson model in one dimension is a quantum particle on a discrete chain of sites with nearest-neighbor hopping and random on-site potentials. It is a progenitor of many further models of disordered systems, and it has spurred numerous…
The aim of this paper is to study the global existence of solutions to a coupled wave-Klein-Gordon system in space dimension two when initial data are small, smooth and mildly decaying at infinity. Some physical models strictly related to…
We consider non smooth general degenerate/singular parabolic equations in non divergence form with degeneracy and singularity occurring in the interior of the spatial domain, in presence of Dirichlet or Neumann boundary conditions. In…
We consider fractional wave equations with exponential or arbitrary polynomial nonlinearities. We prove the global well-posedness on the support of the corresponding Gibbs measures. We provide ill-posedness constructions showing that the…
We give an elementary proof of the global well-posedness for the critical 2D dissipative quasi-geostrophic equation. The argument is based on a non-local maximum principle involving appropriate moduli of continuity.
The nonlinear hyperbolic system of pde's governing the evolution of the deformation of isotropic hyperelastic materials is considered. In the absence of boundaries and with an additional nonresonance or null condition, the system has global…
Recently, there has been a wide interest in the study of aggregation equations and Patlak-Keller-Segel (PKS) models for chemotaxis with degenerate diffusion. The focus of this paper is the unification and generalization of the…
The aim of this work is to show an abstract framework to analyze a family of linear degenerate parabolic mixed equations. We combine the theory for the degenerate parabolic equations with the classical Babuska-Brezzi theory for linear mixed…
In this paper, we first prove global well-posedness for the defocusing cubic nonlinear Schr\"odinger equation (NLS) on 4-dimensional tori - either rational or irrational - and with initial data in $H^1$. Furthermore, we prove that if a…
In this article, we show that the solution to defocusing cubic nonlinear Schr\"odinger equation (NLS) posed on the two-dimensional waveguide \begin{align*} i\partial_tu+\Delta_{\R\times\T}u=|u|^2u \end{align*} is globally well-posed in…
In this paper we consider a nonlinear Petrovsky equation in a bounded domain with a delay term and a strong dissipation \begin{align*} u_{tt} + \Delta^{2} u -\mu_1g_1( \Delta( u_t(x,t))) -\mu_2g_2( \Delta (u_t(x,t-\tau))) =0. \end{align*}…
We prove an invariance principle for the two-dimensional lattice parabolic Anderson model with small potential. As applications we deduce a Donsker type convergence result for a discrete random polymer measure, as well as a universality…
We study the well posedness of the nonlinear Schr\"odinger (NLS) equation with a point interaction and power nonlinearity in dimension two and three. Behind the autonomous interest of the problem, this is a model of the evolution of so…