[Solutions exactes du problème des écoulements instationnaires à surface libre]
Some approach to the solution of boundary value problems for finding functions that are analytical in a wedge is proposed. If the ratio of the angle at the wedge vertex to the number π is rational, then the boundary value problem is reduced to the finite system of ordinary differential equations. Such approach, applied to the problem of inertial motion of a liquid wedge, made it possible to sum the series with small denominators arising in the problem and find four exact examples of self-similar flows with a free boundary.
Une approche permettant de déterminer des fonctions analytiques dans un secteur angulaire et respectant certaines conditions aux limites est proposée. Si le rapport de lʼangle du secteur au nombre π est rationnel, le problème aux limites est réduit à un système fini dʼéquations différentielles ordinaires. Une telle approche, appliquée au problème du mouvement inertiel dʼun secteur liquide, a permis de sommer la série comportant des petits dénominateurs intervenant dans le problème et de trouver quatre exemples exacts dʼécoulements auto-semblables comportant une surface libre.
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Mots-clés : Écoulements limites libres, Petits dénominateurs, Série de pouvoir, Cartographie de conformal
Evgenii Karabut 1
@article{CRMECA_2013__341_6_533_0, author = {Evgenii Karabut}, title = {Exact solutions of the problem of free-boundary unsteady flows}, journal = {Comptes Rendus. M\'ecanique}, pages = {533--537}, publisher = {Elsevier}, volume = {341}, number = {6}, year = {2013}, doi = {10.1016/j.crme.2013.02.009}, language = {en}, }
Evgenii Karabut. Exact solutions of the problem of free-boundary unsteady flows. Comptes Rendus. Mécanique, Volume 341 (2013) no. 6, pp. 533-537. doi : 10.1016/j.crme.2013.02.009. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2013.02.009/
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