Solonnikov, V. A.:
Solvability of two stationary free boundary problems for the Navier-Stokes equations
Bollettino dell'Unione Matematica Italiana Serie 8 1-B (1998), fasc. n.2, p. 283-342, Unione Matematica Italiana (English)
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Si studiano due problemi con frontiera libera per equazioni stazionarie di Navier-Stokes: il problema del movimento di un liquido viscoso incomprimibile generato dalla rotazione di una sbarra rigida immersa nel liquido con velocità angolare assegnata e il problema della fuoriuscita di un liquido da un tubo circolare nello spazio libero. Si assegna l'angolo di contatto tra la frontiera libera e la superficie del tubo e, nel secondo problema, il flusso totale del liquido attraverso l'apertura del tubo. Si dimostra che, nel caso di flusso totale piccolo (oppure della velocità di rotazione piccola), questi problemi possiedono delle soluzioni uniche assi-simmetriche appartenenti ad alcuni spazi di Hölder con peso.
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Con il contributo del Ministero per i Beni e le Attività Culturali