KMS Of Academy of mathematics and systems sciences, CAS
| On Ill- and Well-Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations | |
Hofmanova, Martina1; Zhu, Rongchan2; Zhu, Xiangchan3,4
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| 2021-09-28 | |
| Source Publication | COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
 |
| ISSN | 0010-3640 |
| Pages | 65 |
| Abstract | We are concerned with the question of well-posedness of stochastic, three-dimensional, incompressible Euler equations. In particular, we introduce a novel class of dissipative solutions and show that (i) existence; (ii) weak-strong uniqueness; (iii) nonuniqueness in law; (iv) existence of a strong Markov solution; (v) nonuniqueness of strong Markov solutions: all hold true within this class. Moreover, as a by-product of (iii) we obtain existence and nonuniqueness of probabilistically strong and analytically weak solutions defined up to a stopping time and satisfying an energy inequality. (c) 2021 Wiley Periodicals LLC. |
| DOI | 10.1002/cpa.22023 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme[949981] ; DFG[CRC 1283] ; NSFC[11922103] ; NSFC[11771037] ; NSFC[12090014] ; NSFC[11688101] ; National Key R&D Program of China[2020YFA0712700] ; key Lab of Random Complex Structures and Data Science, Youth Innovation Promotion Association, Chinese Academy of Science[2020003] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied ; Mathematics |
| WOS ID | WOS:000700379000001 |
| Publisher | WILEY |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/59363 |
| Collection | 应用数学研究所 |
| Corresponding Author | Hofmanova, Martina |
| Affiliation | 1.Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany 2.Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China 3.Acad Math & Syst Sci, Beijing, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
| Recommended Citation GB/T 7714 | Hofmanova, Martina,Zhu, Rongchan,Zhu, Xiangchan. On Ill- and Well-Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS,2021:65. |
| APA | Hofmanova, Martina,Zhu, Rongchan,&Zhu, Xiangchan.(2021).On Ill- and Well-Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations.COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS,65. |
| MLA | Hofmanova, Martina,et al."On Ill- and Well-Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations".COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS (2021):65. |
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