3D Burgers equation is an important model for turbulence.It is natural to expect the long-time behaviour for this hydrodynamics equation.However,there is no result about the long-time behaviour for this deterministic ...3D Burgers equation is an important model for turbulence.It is natural to expect the long-time behaviour for this hydrodynamics equation.However,there is no result about the long-time behaviour for this deterministic model.Surprisingly,if the system is perturbed by stochastic noise,we establish the existence and uniqueness of invariant measure for 3D stochastic Burgers equation.展开更多
By comprehensive utilizing of the geometry structure of 2D Burgers equation and the stochastic noise,we find the decay properties of the solution to the stochastic 2D Burgers equation with Dirichlet boundary condition...By comprehensive utilizing of the geometry structure of 2D Burgers equation and the stochastic noise,we find the decay properties of the solution to the stochastic 2D Burgers equation with Dirichlet boundary conditions.Consequently,the expected ergodicity for this turbulence model is established.展开更多
基金supported by National Key R&D Program of China(Grant Nos.2020YFA0712700)NNSF of China(Grant Nos.12090014,11931004,11971077)+3 种基金Key Laboratory of Random Complex Structures and Data Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences(Grant No.2008DP173182)Chongqing Key Laboratory of Analytic Mathematics and Applications,Chongqing UniversityNatural Science Foundation Project of CQ(Grant No.cstc2020jcyj-msxmX0441)Fundamental Research Funds for the Central Universities(Grant No.2020CDJ-LHZZ-027)。
文摘3D Burgers equation is an important model for turbulence.It is natural to expect the long-time behaviour for this hydrodynamics equation.However,there is no result about the long-time behaviour for this deterministic model.Surprisingly,if the system is perturbed by stochastic noise,we establish the existence and uniqueness of invariant measure for 3D stochastic Burgers equation.
基金Supported by National Key R and D Program of China(Grant No.2020YFA0712700)NSFC(Grant Nos.11931004,11971077,12090014)+3 种基金Key Laboratory of Random Complex Structures and Data Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences(Grant No.2008DP173182)Chongqing Key Laboratory of Analytic Mathematics and Applications,Chongqing University,Natural Science Foundation Project of CQ(Grant No.cstc2020jcyjmsxmX0441)Fundamental Research Funds for the Central Universities(Grant No.2020CDJ-LHZZ-027)UIC Start-up Research Fund(Grant No.UICR0700072-24)。
文摘By comprehensive utilizing of the geometry structure of 2D Burgers equation and the stochastic noise,we find the decay properties of the solution to the stochastic 2D Burgers equation with Dirichlet boundary conditions.Consequently,the expected ergodicity for this turbulence model is established.
