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Global regularity for the one-dimensional stochastic Quantum-Navier-Stokes equations

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arxiv 2401.10064 v1 pith:3HVZNKJY submitted 2024-01-18 math.AP

Donatella Donatelli , Lorenzo Pescatore , Stefano Spirito This is my paper · ORCID
classification math.AP
keywords globallocalprovequantum-navier-stokessolutionsstochasticstrongwell-posedness
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In this paper we prove the global in time well-posedness of strong solutions to the Quantum-Navier-Stokes equation driven by random initial data and stochastic external force. In particular, we first give a general local well-posedness result. Then, by means of the Bresch-Desjardins entropy, higher order energy estimates, and a continuation argument we prove that the density never vanishes, and thus that local strong solutions are indeed global.

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  1. Weak martingale solutions to the stochastic 1D Quantum-Navier-Stokes equations

    math.AP 2024-12 conditional novelty 7.0 of 10

    Global weak martingale solutions exist for the stochastic 1D quantum Navier-Stokes equations with density-dependent viscosity and vacuum, for viscosity exponents alpha in (1/2, 1].

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