<p>This work considers the 3-D stochastic fractional Navier-Stokes equation driven by multiplicative noise in critical Fourier-Besov-Morrey spaces <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11565_2025_584_Article_IEq1.gif" Format="GIF" Height="35" Rendition="HTML" Resolution="72" Type="Linedraw" Width="127" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal {F\dot{N}}_{p,h,r}^{1-2\beta +\frac{3}{p^{\prime }}+\frac{h}{p}}(\mathbb {R}^{3})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mrow> <mi mathvariant="script">F</mi> <mover accent="true"> <mi mathvariant="script">N</mi> <mo>˙</mo> </mover> </mrow> <mrow> <mi>p</mi> <mo>,</mo> <mi>h</mi> <mo>,</mo> <mi>r</mi> </mrow> <mrow> <mn>1</mn> <mo>-</mo> <mn>2</mn> <mi>β</mi> <mo>+</mo> <mfrac> <mn>3</mn> <msup> <mi>p</mi> <mo>′</mo> </msup> </mfrac> <mo>+</mo> <mfrac> <mi>h</mi> <mi>p</mi> </mfrac> </mrow> </msubsup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>3</mn> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. We establish the local existence and uniqueness of the solutions to the concerned equation and we prove the global existence in the probabilistic sense when the initial data are small.</p>

Well-posedness for stochastic fractional navier-stokes equation in critical Fourier-Besov-Morrey spaces

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发表日期：

2025年3月15日

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Fatima Ouidirne,
Achraf Azanzal,
Mohamed Oukessou

摘要

This work considers the 3-D stochastic fractional Navier-Stokes equation driven by multiplicative noise in critical Fourier-Besov-Morrey spaces $\mathcal {F\dot{N}}_{p,h,r}^{1-2\beta +\frac{3}{p^{\prime }}+\frac{h}{p}}(\mathbb {R}^{3})$ ${F \dot{N}}_{p, h, r}^{1 - 2 β + \frac{3}{p^{'}} + \frac{h}{p}} (R^{3})$ . We establish the local existence and uniqueness of the solutions to the concerned equation and we prove the global existence in the probabilistic sense when the initial data are small.