Related papers: The dynamic $\Phi^4_3$ model comes down from infin…
We study a rate independent energetic model of the Wilhelmy plate experiment in capillarity. The evolution is driven by vertical motions of the plate. We show stability of energy solutions to the evolution, in the sense used in the…
We prove a frequency-independent bound on trigonometric functions of a class of singular Gaussian random fields, which arise naturally from weak universality problems for singular stochastic PDEs. This enables us to reduce the regularity…
In this paper we study the ergodic theory of a robust non-uniformly expanding maps where no Markov assumption is required. We prove that the topological pressure is differentiable as a function of the dynamics and analytic with respect to…
We study a non-local hydrodynamic system with control. First we characterize the control dynamics as a sub-optimal approximation to the optimal control problem constrained to the evolution of the pressureless Euler alignment system. We then…
Consider the radial nonlinear wave equation $-\partial_t^2 u + \Delta u = u^3$, $u :\mathbb{R}_t \times \mathbb{R}_x^3 \to \mathbb{R}$, $u(t,x) = u(t,|x|)$. In this paper, we construct a Gibbs measure for this system and prove its…
A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the…
We consider the continuum parabolic Anderson model (PAM) and the dynamical $\Phi^4$ equation on the $3$-dimensional cube with boundary conditions. While the Dirichlet solution theories are relatively standard, the case of Neumann/Robin…
The exact solution for the thermodynamic and dynamic properties of the infinite-dimensional multi-component Falicov-Kimball model for arbitrary concentration of d- and f-electrons is presented. The emphasis is on a descriptive derivation of…
We consider the dynamics of systems of lattice bosons with infinitely many degrees of freedom. We show that their dynamics defines a group of automorphisms on a $C^*$--algebra introduced by Buchholz, which extends the resolvent algebra of…
We prove the immediate appearance of a lower bound for mild solutions to the full Boltzmann equation in the torus or a $C^2$ convex domain with specular boundary conditions, under the sole assumption of continuity away from the grazing set…
In this paper we are concerned with a non-isothermal compressible Navier-Stokes-Fourier model with density dependent viscosity that vanish on the vacuum. We prove the global existence of weak solutions with large data in the…
In this paper we prove well-posedness for a measure-valued continuity equation with solution-dependent velocity and flux boundary conditions, posed on a bounded one-dimensional domain. We generalize the results of [Evers, Hille and Muntean.…
We consider the dynamics of a vertically stratified, horizontally-forced Kolmogorov flow. Motivated by astrophysical systems where the Prandtl number is often asymptotically small, our focus is the little-studied limit of high Reynolds…
We consider the mixing properties of solutions to the advection-diffusion equation of a white-in-time velocity field on the 2-dimensional torus with four forced modes. As the diffusivity parameter goes to zero, we show that the almost-sure…
In this paper, we consider an incompressible viscous flow without surface tension in a finite-depth domain of three dimensions, with free top boundary and fixed bottom boundary. This system is governed by a Naiver-Stokes equation in above…
A new numerical framework, based on the use of a simple first order strongly hyperbolic evolution equations, is introduced and tested in case of 4-dimensional spherically symmetric gravitating systems. The analytic setup is chosen such that…
We define the topological entropy per unit volume in parabolic PDE's such as the complex Ginzburg-Landau equation, and show that it exists, and is bounded by the upper Hausdorff dimension times the maximal expansion rate. We then give a…
Presented are two results on the formation of finite time singularities of solutions to the compressible Euler equations in two and three space dimensions for isentropic, polytropic, ideal fluid flows. The initial velocity is assumed to be…
We consider the fractional $\Phi^3_d$-measure on the $d$-dimensional torus, with Gaussian free field having inverse covariance $(1-\Delta)^\alpha$, and show a phase transition at $d=3\alpha$. More precisely, in a regular regime $d<3\alpha$,…
We prove that for every locally stable and tempered pair potential $\phi$ with bounded range, there exists a unique infinite-volume Gibbs point process on $\mathbb{R}^d$ for every activity $\lambda < (e^{L} \hat{C}_{\phi})^{-1}$, where $L$…