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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.…
Multi-level Monte Carlo Finite Difference Methods for Fractional Conservation Laws with Random Data
Ujjwal Koley, Deep Ray, Tanmay Sarkar
We establish a notion of random entropy solution for degenerate fractional conservation laws incorporating randomness in the initial data, convective flux and diffusive flux. In or…
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…