TITLE:
Martingale Solution to Stochastic Extended Korteweg-de Vries Equation
AUTHORS:
Anna Karczewska, Maciej Szczeciński
KEYWORDS:
Extended Korteweg-de Vries Equation, Martingale Solution, Stochastic Fluid Dynamics
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.8 No.12,
December
26,
2018
ABSTRACT: 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.