Abstract
We consider the stochastic Navier–Stokes equations in \({\mathbb T}^{3}\) with multiplicative white noise. We construct a unique local strong solution with initial data in \(L^p\), where \(p>5\). We also address the global existence of the solution when the initial data is small in \(L^p\), with the same range of p.
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Acknowledgements
IK was supported in part by the NSF Grant DMS-1907992. FX would like to thank the Hausdorff Research Institute for Mathematics for their hospitality during her work on this paper.
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Kukavica, I., Xu, F. & Ziane, M. Global existence for the stochastic Navier–Stokes equations with small \(L^{p}\) data. Stoch PDE: Anal Comp 10, 160–189 (2022). https://doi.org/10.1007/s40072-021-00196-9
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DOI: https://doi.org/10.1007/s40072-021-00196-9