Related papers: A universal total anomalous dissipator

As a solvable and broadly applicable model system, the totally asymmetric exclusion process enjoys iconic status in the theory of non-equilibrium phase transitions. Here, we focus on the time dependence of the total number of particles on a…

A multispecies, collisionless plasma is modeled by the Vlasov-Poisson system. Assuming that the electric field decays with sufficient rapidity as $t \to\infty$, we show that the velocity characteristics and spatial averages of the particle…

We present a characterization of the asymptotics of all asymptotically flat stationary vacuum solutions of Einstein's field equations. This characterization is given in terms of two sequences of symmetric trace free tensors (we call them…

In its customary formulation for one-component fluids, the Hierarchical Reference Theory yields a quasilinear partial differential equation for an auxiliary quantity f that can be solved even arbitrarily close to the critical point,…

We study the asymptotic behaviour of families of gradient flows in a general metric setting, when the metric-dissipation potentials degenerate in the limit to a dissipation with linear growth. We present a general variational definition of…

In the Cauchy problem for asymptotically flat vacuum data the solution-jets along the cylinder at space-like infinity develop in general logarithmic singularities at the critical sets at which the cylinder touches future/past null infinity.…

In this paper, we characterize all the distributions $F \in \mathcal{D}'(U)$ such that there exists a continuous weak solution $v \in C(U,\mathbb{C}^{n})$ (with $U \subset \Omega$) to the divergence-type equation…

This paper deals with the oncolytic virotherapy model \begin{equation}\begin{split} \begin{cases} &u_t = \Delta u - \nabla \cdot (u\nabla v)-uz +\mu u(1-u),& \\[2ex] &v_t = - (u+w)v,& \\[2ex] &w_t = D_w \Delta w - w + uz,& \\[2ex] &z_t =…

We propose fully discrete, implicit-in-time finite-volume schemes for a general family of non-linear and non-local Fokker-Planck equations with a gradient-flow structure, usually known as aggregation-diffusion equations, in any dimension.…

Given $s\in (3/2,2)$ and $\varepsilon >0$, we construct a compactly supported initial data $\theta_0$ such that $\| \theta_0 \|_{H^s}\leq \varepsilon$ and there exist $T>0$, $c>0$ and a local-in-time solution $\theta$ of the SQG equation…

This paper studies the existence and uniqueness of local weak solutions to the d-dimensional tropical climate model without thermal diffusion. We establish that, when $\alpha=\beta\geq1$, $\eta=0$, any initial data $(u_{0},v_{0})\in…

We construct global generalized solutions to the chemotaxis system \begin{align*} \begin{cases} u_t = \Delta u - \nabla \cdot (u \nabla v) + \lambda(x) u - \mu(x) u^\kappa,\\ v_t = \Delta v - v + u \end{cases} \end{align*} in smooth,…

We show that for a contact Anosov flow on a compact manifold $ M $, the solutions to $ \partial_t u + X u = \nu \Delta u $, $ \nu > 0 $, where $ X $ is the generator of the flow and $ \Delta $, a (negative) Laplacian for some Riemannian…

We discuss the structure of 2D conformal field theories (CFT) at central charge c=0 describing critical disordered systems, polymers and percolation. We construct a novel extension of the c=0 Virasoro algebra, characterized by a number b…

We find a new scaling invariance of the barotropic compressible Navier-Stokes equations. Then it is shown that type I singularities of solutions with $$\limsup_{t \nearrow T}|{\rm div} u(t, x)|(T - t) \leq \kappa,$$ can never happen at time…

In this paper, we study the asymptotic behaviors of solutions to the inhomogeneous Navier-Stokes-Vlasov system in $\mathbb{R}^{3}\times\mathbb{R}^{3}$, where the initial fluid density is allowed to vanish. We establish the uniform bound of…

We study the well-posedness and the spatial behavior at infinity of perfect fluid flows on $\R^d$ with initial data in a scale of weighted Sobolev spaces that allow spatial growth/decay at infinity as $|x|^\beta$ with $\beta<1/2$. In…

We show that every modular differential equation of a rational conformal field theory comes from a null vector in the vacuum Verma module. We also comment on the implications of this result for the consistency of the extremal self-dual…

Using a weak convergence approach, we establish a Large Deviation Principle (LDP) for the solutions of fluid dynamic systems in two-dimensional bounded domains subjected to no-slip boundary conditions and perturbed by additive noise. Our…

In an optimal control framework, we consider the value $V_T(x)$ of the problem starting from state $x$ with finite horizon $T$, as well as the value $V_\lambda(x)$ of the $\lambda$-discounted problem starting from $x$. We prove that uniform…