Abstract
We are concerned with the power-law fluids driven by an additive stochastic forcing in dimension d⩾3. For the power index r∈(1,3d+2d+2), we establish existence of infinitely many global-in-time probabilistically strong and analytically weak solutions in Llocp([0,∞);L2)∩C([0,∞);W1,max{1,r−1}),p⩾1 for every divergence free initial condition in L2∩W1,max{1,r−1}. This result in particular implies non-uniqueness in law. Our result is sharp in the three dimensional case in the sense that the solution is unique if r⩾3d+2d+2.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.