TY - JOUR
T1 - Global martingale solution for the stochastic Boussinesq system with zero dissipation
AU - Yamazaki, Kazuo
N1 - Publisher Copyright:
© 2016 Taylor & Francis Group, LLC.
PY - 2016/5/3
Y1 - 2016/5/3
N2 - ABSTRACT: We study the two-dimensional stochastic Boussinesq system with zero dissipation and multiplicative noise. We show the existence of a martingale solution by a priori estimates using stochastic calculus, and applications of Prokhorov's, Skorokhod's, and martingale representation theorems. Due to the lack of dissipation, the proof requires higher regularity estimates, taking advantage of the structure of the nonlinear term. Moreover, we obtain the existence of the pressure term via an application of de Rham's theorem for processes.
AB - ABSTRACT: We study the two-dimensional stochastic Boussinesq system with zero dissipation and multiplicative noise. We show the existence of a martingale solution by a priori estimates using stochastic calculus, and applications of Prokhorov's, Skorokhod's, and martingale representation theorems. Due to the lack of dissipation, the proof requires higher regularity estimates, taking advantage of the structure of the nonlinear term. Moreover, we obtain the existence of the pressure term via an application of de Rham's theorem for processes.
KW - Boussinesq system
KW - Navier–Stokes equations
KW - Prokhorov's theorem
KW - Skorokhod's theorem
KW - martingale solution
UR - http://www.scopus.com/inward/record.url?scp=84964066724&partnerID=8YFLogxK
U2 - 10.1080/07362994.2016.1148615
DO - 10.1080/07362994.2016.1148615
M3 - Article
AN - SCOPUS:84964066724
SN - 0736-2994
VL - 34
SP - 404
EP - 426
JO - Stochastic Analysis and Applications
JF - Stochastic Analysis and Applications
IS - 3
ER -