11 research outputs found

    On bilinear estimates and critical uniqueness classes for Navier-Stokes equations

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    We are concerned with bilinear estimates and uniqueness of mild solutions for the Navier-Stokes equations in critical persistence spaces. For that, we construct general settings in which estimates for the bilinear term of the mild formulation hold true without using auxiliary norms such as Kato time-weighted ones. We first obtain necessary conditions in abstract critical spaces and after consider settings with further structure to obtain the estimates in general classes of Besov, Morrey and Besov-Morrey spaces based on Banach spaces. We then give examples and applications of the abstract theory, which contribute with different proofs for some known estimates, and consequently for the corresponding uniqueness property, and contain (as far as we know) a new bilinear estimate in Besov-weak-Herz spaces. Some ingredients of our approach are characterizations and estimates on the corresponding predual spaces. In addition, we present applications of the theory to other PDEs.Comment: 36 page

    Outcomes from elective colorectal cancer surgery during the SARS-CoV-2 pandemic

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    This study aimed to describe the change in surgical practice and the impact of SARS-CoV-2 on mortality after surgical resection of colorectal cancer during the initial phases of the SARS-CoV-2 pandemic

    Ultralight vector dark matter search using data from the KAGRA O3GK run

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    Among the various candidates for dark matter (DM), ultralight vector DM can be probed by laser interferometric gravitational wave detectors through the measurement of oscillating length changes in the arm cavities. In this context, KAGRA has a unique feature due to differing compositions of its mirrors, enhancing the signal of vector DM in the length change in the auxiliary channels. Here we present the result of a search for U(1)B−L gauge boson DM using the KAGRA data from auxiliary length channels during the first joint observation run together with GEO600. By applying our search pipeline, which takes into account the stochastic nature of ultralight DM, upper bounds on the coupling strength between the U(1)B−L gauge boson and ordinary matter are obtained for a range of DM masses. While our constraints are less stringent than those derived from previous experiments, this study demonstrates the applicability of our method to the lower-mass vector DM search, which is made difficult in this measurement by the short observation time compared to the auto-correlation time scale of DM

    Observation of gravitational waves from the coalescence of a 2.5−4.5 M⊙ compact object and a neutron star

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