arXiv subjects

Soumya Ranjan Behera

Publications and source records attributed to Soumya Ranjan Behera.

6 recordsLinked to original sources

arXiv2026

Error analysis for 3D Navier--Stokes equations with additive noise

We consider the three-dimensional stochastic Navier--Stokes equations with additive stochastic forcing. We study temporal discretizations based on a semi-implicit Euler as well as a Crank-Nicolson scheme. We prove that locally in time the former converges with rate 1 while the latter converges with rate 3/2. These theoretical results are confirmed by extensive numerical simulations. To the best of our knowledge this is the first time that numerical simulations for the three-dimensional stochastic Navier--Stokes equations have been performed.

math.NA↗

arXiv2024

Renormalized stochastic entropy solution for degenerate parabolic-hyperbolic equations with Levy noise

In this article, we establish the well-posedness theory for renormalized entropy solutions of a degenerate parabolic-hyperbolic PDE perturbed by a multiplicative Levy noise with general L1-data on the unbounded domain. By using a suitable approximation procedure based on the vanishing viscosity technique and bounded data, we prove the existence of a renormalized entropy solution to the underlying problem. The uniqueness of the solution is settled by adapting Kružkov's doubling the variables technique in the presence of noise.

math.AP↗

arXiv2024

Homogeneous Dirichlet problem for degenerate parabolic-hyperbolic PDE driven by Levy noise

In this article, we study the homogeneous Dirichlet problem for a degenerate parabolic-hyperbolic PDE perturbed by Levy noise. In particular, we develop the well-posedness theory of entropy solution based on the Kružkov's semi-entropy formulation. In comparison to the pioneered work by Bauzet et al. (J. Funct. Anal. 266, (2014), 2503-2545), concerning the existence and uniqueness of entropy solution for the Dirichlet problem for conservation laws driven by Brownian noise, our present analysis involves a simpler approach to obtain the global Kato's inequality.

math.AP↗

arXiv2023

On rate of convergence of finite difference scheme for degenerate parabolic-hyperbolic PDE with Levy noise

In this article, we consider a semi discrete finite difference scheme for a degenerate parabolic-hyperbolic PDE driven by Lévy noise in one space dimension. Using bounded variation estimations and a variant of classical Kružkov's doubling of variable approach, we prove that expected value of the $L^1$-difference between the unique entropy solution and approximate solution converges at a rate of $(Δx)^\frac{1}{7}$, where $Δx$ is the spatial mesh size.

math.NA↗

arXiv2023

Stochastic Fractional Conservation Laws: Large deviation principle, Central limit theorem and Moderate deviation principle

In this article, we establish the Freidlin-Wentzell type large deviation principle and central limit theorem for stochastic fractional conservation laws with small multiplicative noise in kinetic formulation framework. The weak convergence method and doubling variables method play a crucial role. As a consequence, we also establish moderate deviation principle for the underlying problem.

math.PR↗

arXiv2023

Convergence of an operator splitting scheme for fractional conservation laws with Levy noise

In this paper, we are concerned with a operator splitting scheme for linear fractional and fractional degenerate stochastic conservation laws driven by multiplicative Levy noise. More specifically, using a variant of classical Kruzkov's doubling of variable approach, we show that the approximate solutions generated by the splitting scheme converges to the unique stochastic entropy solution of the underlying problems.Finally, the convergence analysis is illustrated by several numerical examples.

math.NA↗