Utpal Manna

LARGE DEVIATIONS FOR THE STOCHASTIC SHELL MODEL OF TURBULENCE

In this work, we first prove the existence and uniqueness of a strong solution to stochastic GOY model of turbulence with a small multiplicative noise. Then using the weak convergence approach, Laplace principle for solutions of the stochastic GOY model is established in certain Polish space. Thus a Wentzell–Freidlin type large deviation principle is established utilizing certain results by Varadhan and Bryc.

STOCHASTIC ANALYSIS OF TIDAL DYNAMICS EQUATION

In this paper the deterministic and stochastic tidal equation in 2-D have been studied. The main results of this work are the existence and uniqueness theorem for strong solutions. These results are obtained by utilizing a global monotonicity property of the sum of the linear and nonlinear operators and exploiting the generalized Minty-Browder technique.

Cooperation in Transboundary Water Sharing Under Climate Change

As multiple countries share a river, the likelihood of a water resource conflict from climate change could be higher between countries. In this paper, we demonstrate how countries can cooperate in transboundary water sharing in a sustainable way, given the impacts of climate change. We illustrate the case of water sharing of the Volta River between the upstream and downstream country, Burkina Faso and Ghana respectively, where the latter country faces a tradeoff of water use between agriculture in the north and production of hydro energy in the south. In the framework of a stochastic Stackelberg differential game, we have shown how the issue of water sharing could be linked to hydropower export that can make water sharing between the countries sustaining in the event of climate change. Our results indicate that during cooperation, Ghana will have an opportunity to increase its water abstraction for agriculture, which has remained largely restricted. We also find that the equilibrium strategies in the long run steady state distribution are stable even with increasing variances of water flow.

Stochastic non-resistive magnetohydrodynamic system with L\'{e}vy noise

Abstract In this work we prove the existence and uniqueness of path-wise solutions up to a maximal time for the viscous, non-resistive stochastic magnetohydrodynamic system perturbed by Lévy noise in two and three dimensions. The local-in-time existence and uniqueness result for the ideal and non-viscous MHD equations with Lévy noise is also addressed.

Stochastic Navier–Stokes Equations in Unbounded Channel Domains

In this paper we prove the existence and uniqueness of path-wise strong solution to stochastic viscous flow in unbounded channels with multiple outlets using local monotonicity arguments. We devise a construction for solvability using a stochastic basic vector field.