Searcharxiv⌕ Search

arXiv subjects

Misha Neklyudov

Publications and source records attributed to Misha Neklyudov.

5 recordsLinked to original sources
arXiv2014

Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere

We study ergodic properties of stochastic geometric wave equations on a particular model with the target being the 2D sphere while considering the space variable-independent solutions only. This simplification leads to a degenerate stochastic equation in the tangent bundle of the 2D sphere. Studying this equation, we prove existence and non-uniqueness of invariant probability measures for the original problem and we obtain also results on attractivity towards an invariant measure. We also present a suitable numerical scheme for approximating the solutions subject to a sphere constraint.

math.PR↗
arXiv2012

Multidimensional stochastic Burgers equation

We consider multidimensional stochastic Burgers equation on the torus $\mathbb{T}^d$ and the whole space $\Rd$. In both cases we show that for positive viscosity $ν>0$ there exists a unique strong global solution in $L^p$ for $p>d$. In the case of torus we also establish a uniform in $ν$ a priori estimate and consider a limit $ν\todown 0$ for potential solutions. In the case of $\Rd$ uniform with respect to $ν$ a priori estimate established if a Beale-Kato-Majda type condition is satisfied.

math-ph↗
arXiv2011

Conservative interacting particles system with anomalous rate of ergodicity

We analyze certain conservative interacting particle system and establish ergodicity of the system for a family of invariant measures. Furthermore, we show that convergence rate to equilibrium is exponential. This result is of interest because it presents counterexample to the standard assumption of physicists that conservative system implies polynomial rate of convergence.

math.PR↗
arXiv2008

Beale-Kato-Majda type condition for Burgers equation

We consider a multidimensional Burgers equation on the torus $\mathbb{T}^d$ and the whole space $\Rd$. We show that, in case of the torus, there exists a unique global solution in Lebesgue spaces. For a torus we also provide estimates on the large time behaviour of solutions. In the case of $\Rd$ we establish the existence of a unique global solution if a Beale-Kato-Majda type condition is satisfied. To prove these results we use the probabilistic arguments which seem to be new.

math.AP↗