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Unbounded rough drivers, rough PDEs and applications

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arxiv 2501.01186 v2 pith:WNB6LQNE submitted 2025-01-02 math.AP math.PR

Antoine Hocquet , Martina Hofmanova , Torstein Nilssen This is my paper · ORCID
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keywords roughapplicationsequationsunboundedconcretecontributionsdifferentialdriver
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A summary of recent contributions in the field of rough partial differential equations is given. For that purpose we rely on the formalism of ``unbounded rough driver''. We present applications to concrete models including Landau-Lifshitz-Gilbert, Navier-Stokes and Euler equations.

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  1. On the well-posedness of (nonlinear) rough continuity equations

    math.AP 2025-02 accept novelty 8.0 of 10

    Rough continuity and transport equations are well-posed for Osgood and DiPerna-Lions drifts, yielding a rough Yudovich theorem for 2D Euler and a continuous random dynamical system.

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