@prefix dcat: <http://www.w3.org/ns/dcat#> .
@prefix dct: <http://purl.org/dc/terms/> .
@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix vcard: <http://www.w3.org/2006/vcard/ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

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              We propose a practical nonlinear open boundary condition of Robin type for unsteady incompressible viscous flows taking account of the local inflow/outflow volume rate at an open artificial boundary with a singular load. The inflow/outflow parameters introduced in the modelling can be connected to the coefficient of singular head loss through Bernouilli's theorem of energy balance in a curl-free viscous flow. Then, we prove that this boundary condition leads to a well-posed unsteady nonlinear Stokes problem, i.e. global in time existence of a weak solution in dimension $d\\leq 3$ with no restriction on the data. The proof is carried out by passing to the limit on a sequence of consistent discrete solutions of a non linear numerical scheme which approximates the original problem. The main ingredients are Schauder's fixed-point theorem and Aubin-Lions compactness argument.
            """ ;
    dct:identifier "hal-00820404" ;
    dct:issued "2026-05-11T05:28:44.107998"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-11T05:28:44.108004"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "On the unsteady Stokes problem with a nonlinear open artificial boundary condition modelling a singular load" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
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    dcat:keyword "2010-msc-35a35-35j50-35j60-35j65-35k40-35k55-35k60-35q30-76d03-76d05-65m06-65m12-65n12",
        "artificial-boundary",
        "inflowoutflow-boundary-condition",
        "infoeu-reposemanticspreprint",
        "infoinfo-mocomputer-science-csmodeling-and-simulation",
        "mathmath-apmathematics-mathanalysis-of-pdes-mathap",
        "mathmath-namathematics-mathnumerical-analysis-mathna",
        "non-stationary-stokes-problem",
        "open-boundary-condition",
        "physmecameflphysics-physicsmechanics-physicsfluid-mechanics-physicsclass-ph",
        "physphysphys-flu-dynphysics-physicsphysics-physicsfluid-dynamics-physicsflu-dyn",
        "preprints-working-papers-",
        "singular-head-loss",
        "spimecameflengineering-sciences-physicsmechanics-physicsmed-phfluids-mechanics-physicsc",
        "unsteady-incompressible-viscous-flow" ;
    dcat:landingPage <https://hal.science/hal-00820404> .

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    dct:issued "2026-05-11T05:28:44.134594"^^xsd:dateTime ;
    dct:modified "2026-05-11T05:28:44.091974"^^xsd:dateTime ;
    dct:title "On the unsteady Stokes problem with a nonlinear open artificial boundary condition modelling a singular load" ;
    dcat:accessURL <https://hal.science/hal-00820404> .

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