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Non-uniqueness in law of transport-diffusion equation forced by random noise
Ujjwal Koley, Kazuo Yamazaki
We consider a transport-diffusion equation forced by random noise of three types: additive, linear multiplicative in It's interpretation, and transport in Straton…
On the rate of convergence of a numerical scheme for fractional conservation laws with noise
Ujjwal Koley, Guy Vallet
We consider a semi-discrete finite volume scheme for a degenerate fractional conservation laws driven by a cylindrical Wiener process. Making use of the bounded variation (BV) esti…
A convergent finite volume scheme for the stochastic barotropic compressible Euler equations
Abhishek Chaudhary, Ujjwal Koley
In this paper, we analyze a semi-discrete finite volume scheme for the three-dimensional barotropic compressible Euler equations driven by a multiplicative Brownian noise. We deriv…
On weak-strong uniqueness for stochastic equations of incompressible fluid flow
Abhishek Chaudhary, Ujjwal Koley
We introduce a novel concept of dissipative measure-valued martingale solution to the stochastic Euler equations describing the motion of an inviscid incompressible fluid. These so…
Measure-valued solutions to the stochastic compressible Euler equations and incompressible limits
Martina Hofmanova, Ujjwal Koley, Utsab Sarkar
We introduce a new concept of dissipative measure-valued martingale solutions to the stochastic compressible Euler equations. These solutions are weak in the probabilistic sense i.…
A fractional degenerate parabolic-hyperbolic Cauchy problem with noise
Neeraj Bhauryal, Ujjwal Koley, Guy Vallet
We consider the Cauchy problem for a stochastic scalar parabolic-hyperbolic equation in any space dimension with nonlocal, nonlinear, and possibly degenerate diffusion terms. The e…