Author(s)

Anna Karczewska, Maciej Szczeciński

Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Zielona Góra, Poland.

The deterministic extended Korteweg-de Vries equation plays an essential role in the description of the creation and propagation of nonlinear waves in many fields. We study a stochastic extended Korteweg-de Vries equation driven by a multiplicative noise in the form of a cylindrical Wiener process. We prove the existence of a martingale solution to the equation studied for all physically relevant initial conditions. The proof of the solution is based on two approximations of the problem considered and the compactness method.

Extended Korteweg-de Vries Equation, Martingale Solution, Stochastic Fluid Dynamics

Karczewska, A. and Szczeciński, M. (2018) Martingale Solution to Stochastic Extended Korteweg-de Vries Equation. Advances in Pure Mathematics, 8, 863-878. doi: 10.4236/apm.2018.812053.