We study strong ratio limit properties of the quotients of the heat kernels of subcritical and critical operators which are defined on a noncompact Riemannian manifold.
This paper addresses the mathematical models for the heat-conduction equations and the Navier-Stokes equations via fractional derivatives without singular kernel.
We prove almost sure Euler hydrodynamics for a large class of attractive particle systems on $Z$ starting from an arbitrary initial profile. We generalize earlier works by Seppalainen (1999) and Andjel et al. (2004). Our constructive approach require
s new ideas since the subadditive ergodic theorem (central to previous works) is no longer effective in our setting.
In this paper we prove the convergence of solutions to discrete models for binary waveguide arrays toward those of their formal continuum limit, for which we also show the existence of localized standing waves. This work rigorously justifies formal a
rguments and numerical simulations present in the Physics literature.
In this paper, we consider the mean field limit of Brownian particles with Coulomb interaction in 3D space. In particular, using a symmetrization technique, we show that the limit measure almost surely is a weak solution to the limiting nonlinear Fok
ker-Planck equation. By proving that the energy almost surely is bounded by the initial energy, we improve the regularity of the weak solutions. Moreover, by a natural assumption, we establish the weak strong uniqueness principle, which is closely related to the propagation of chaos.
We give fully explicit upper and lower bounds for the constants in two known inequalities related to the quadratic nonlinearity of the incompressible (Euler or) Navier-Stokes equations on the torus T^d. These inequalities are tame generalizations (in
the sense of Nash-Moser) of the ones analyzed in the previous works [Morosi and Pizzocchero: CPAA 2012, Appl.Math.Lett. 2013].