Global-in-time probabilistically strong solutions to stochastic power-law equations: Existence and non-uniqueness

Huaxiang Lü and Xiangchan Zhu

Stochastic Processes and their Applications, 2023, vol. 164, issue C, 62-98

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.

Keywords: Stochastic power-law equations; Probabilistically strong solutions; Non-uniqueness in law; Convex integration (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414923001357
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:164:y:2023:i:c:p:62-98

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2023.06.014

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().