TY - JOUR
T1 - Global well-posedness and large deviations for 3D stochastic Burgers equations
AU - Zhang, Rangrang
AU - Zhou, Guoli
AU - Guo, Boling
AU - Wu, Jianglun
N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020/2/1
Y1 - 2020/2/1
N2 - In this paper, we study the stochastic vector-valued Burgers equations with non-periodic boundary conditions. We first apply a contraction principle argument to show local existence and uniqueness of a mild solution to this model. Then, toward obtaining the global well-posedness, we derive a priori estimates of the local solution by utilizing the maximum principle. Finally, we establish, by means of the weak convergence approach, the Freidlin–Wentzell type large deviation principle for 3D stochastic Burgers equations when the noise term goes to zero.
AB - In this paper, we study the stochastic vector-valued Burgers equations with non-periodic boundary conditions. We first apply a contraction principle argument to show local existence and uniqueness of a mild solution to this model. Then, toward obtaining the global well-posedness, we derive a priori estimates of the local solution by utilizing the maximum principle. Finally, we establish, by means of the weak convergence approach, the Freidlin–Wentzell type large deviation principle for 3D stochastic Burgers equations when the noise term goes to zero.
KW - 3D stochastic Burgers equations
KW - Global well-posedness
KW - The Freidlin–Wentzell type large deviation principle
UR - http://www.scopus.com/inward/record.url?scp=85078481072&partnerID=8YFLogxK
U2 - 10.1007/s00033-020-1259-z
DO - 10.1007/s00033-020-1259-z
M3 - Article
AN - SCOPUS:85078481072
SN - 0044-2275
VL - 71
JO - Zeitschrift fur Angewandte Mathematik und Physik
JF - Zeitschrift fur Angewandte Mathematik und Physik
IS - 1
M1 - 30
ER -