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Well-Posedness for Stochastic Fractional Navier–Stokes Equation in the Critical Fourier–Besov Space
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Guangjun Shen
Journal of Theoretical Probability, Volume: 35, Issue: 4
Swansea University Author:
Jiang-lun Wu
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DOI (Published version): 10.1007/s10959-021-01152-y
Abstract
This paper concerns the three-dimensional multiplicative stochastic fractional Navier-Stokesequation. Using Fourier localization technique, we establish the local existence and uniqueness of the solutions in the critical Fourier-Besov space $\mathcal{\dot{B}}^{4-2\alpha-\frac{3}{p}}_{p,r}$. Moreover...
| Published in: | Journal of Theoretical Probability |
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| ISSN: | 0894-9840 1572-9230 |
| Published: |
Springer Science and Business Media LLC
2022
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa58983 |
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| Abstract: |
This paper concerns the three-dimensional multiplicative stochastic fractional Navier-Stokesequation. Using Fourier localization technique, we establish the local existence and uniqueness of the solutions in the critical Fourier-Besov space $\mathcal{\dot{B}}^{4-2\alpha-\frac{3}{p}}_{p,r}$. Moreover, when the initial date is sufficiently small, we obtain the global existence of the solutions in probability. |
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| Keywords: |
stochastic fractional Navier-Stokes equation; Fourier-Besov space; strong solution. |
| College: |
Faculty of Science and Engineering |
| Funders: |
Natural Science Foundation of China (Nos.11901005 and 12071003) and the Natural Science Foundation of Anhui Province (No. 2008085QA20) |
| Issue: |
4 |