Related papers: Note on the dissipation for the general Muskat pro…
We prove an equidistribution result for torsion points of Drinfeld modules of generic characteristic. We also show that similar equidistribution statements provide proofs for the Manin-Mumford and the Bogomolov conjectures for Drinfeld…
We prove that the 3D stable Muskat problem is globally well-posed in the critical Sobolev space $\dot H^2 \cap \dot W^{1,\infty}$ provided that the semi-norm $\Vert f_0 \Vert_{\dot H^{2}}$ is small enough. Consequently, this allows the…
We survey a variety of cosmological problems where the issue of generality has arisen. This is aimed at providing a wider context for many claims and deductions made when philosophers of science choose cosmological problems for…
We study the condensation phenomenon for the invariant measures of the mean-field model of reversible coagulation-fragmentation processes conditioned to a supercritical density of particles. It is shown that when the parameters of the…
We address the question of global in time existence of solutions to a magnetoviscoelastic system with general initial data. We show that the notion of dissipative solutions allows to prove such an existence in two and three dimensions. This…
The evolution of a two-phase Hele-Shaw problem, a Muskat problem, under assumption of a negligible surface tension is considered. We use the Schwarz function approach and allow the sinks and sources to be line distributions with disjoint…
Following Abbatiello et al. [ DCCDS-A (41), 2020], we introduce dissipative turbulent solutions to a simple model of a mixture of two non interacting compressible fluids {\tc filling a bounded domain with general non zero inflow/outflow…
The influence of dissipation on the fluctuation statistics of the total energy is investigated through both a phenomenological and a stochastic model for dissipative energy-transfer through a cascade of states. In equilibrium the states…
A quantum mechanical model is used to derive a generalized Landau-Lifshitz equation for a magnetic moment, including fluctuations and dissipation. The model reproduces the Gilbert-Brown form of the equation in the classical limit. The…
This paper shows that the ordinary Jeans wave number can be obtained as a limiting case of a more general approach that includes dissipative effects. Corrections to the Jeans critical mass associated to viscosity are established. Some…
We show a new Bernstein's inequality which generalizes the results of Cannone-Planchon, Danchin and Lemari\'{e}-Rieusset. As an application of this inequality, we prove the global well-posedness of the 2D quasi-geostrophic equation with the…
We give a generalization of the Shestakov-Umirbaev inequality which plays an important role in their solution of the tame generators conjecture.
Based on the central limit theorem, we discuss the problem of evaluation of the statistical error of Monte Carlo calculations using a time discretized diffusion process. We present a robust and practical method to determine the effective…
We study the two-dimensional multiphase Muskat problem describing the motion of three immiscible fluids with equal viscosities in a vertical homogeneous porous medium identified with $\mathbb{R}^2$ under the effect of gravity. We first…
The Muskat problem models the evolution of the interface given by two different fluids in porous media. The Rayleigh-Taylor condition is natural to reach the linear stability of the Muskat problem. We show that the Rayleigh-Taylor condition…
The possibility of dissipative contributions to the mass flux is considered in detail. A general, thermodynamically consistent framework is developed to obtain such terms, the compatibility of which with general principles is then…
We present the constraint for the discrete Moutard equation which gives the integrable discretization of the Bianchi-Ernst system. We also derive the discrete analogue of the Bianchi transformation between solutions of such a system (the…
We study a model of a general compressible viscous fluid subject to the Coulomb friction law boundary condition. For this model, we introduce a dissipative formulation and prove the existence of dissipative solutions. The proof of this…
In this paper we consider second order evolution equations with bounded damping. We give a characterization of a non uniform decay for the damped problem using a kind of observability estimate for the associated undamped problem.
The Riccati inequality and equality are studied for infinite dimensional linear discrete time stationary systems with respect to the scattering supply rate. The results obtained are an addition to and based on our earlier work on the…