A stochastic representation for backward incompressible Navier-Stokes equations

作者：Zhang Xicheng^*

来源：Probability Theory and Related Fields, 2010, 148(1-2): 305-332.

DOI：10.1007/s00440-009-0234-6

• Backward Navier-Stokes equation
• Stochastic representation
• Global existence
• Large deviation

By reversing the time variable we derive a stochastic representation for backward incompressible Navier-Stokes equations in terms of stochastic Lagrangian paths, which is similar to Constantin and Iyer's forward formulations in Constantin and Iyer (Comm Pure Appl Math LXI:330-345, 2008). Using this representation, a self-contained proof of local existence of solutions in Sobolev spaces are provided for incompressible Navier-Stokes equations in the whole space. In two dimensions or large viscosity, an alternative proof to the global existence is also given. Moreover, a large deviation estimate for stochastic particle trajectories is presented when the viscosity tends to zero.

• 出版日期2010-9
• 单位华中科技大学