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Existence and uniqueness of solutions for linear conservation laws with velocity field in L∞

2005, Besson, Olivier, Pousin, Jérôme

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Hele-Shaw approximation for resin transfer molding

2005, Besson, Olivier, Pousin, Jérôme

A Hele-Shaw flow is studied as the limit of a Stokes flow. The velocity fields associated to each fluid solve a fluid dynamic problem with time dependent domain. The moving boundary formulation is based on a pseudo-concentration equation. Some existence of solution of this set of equations is given using the classical Leary-Schauder Theorem and the use of space-time integrated least square method for the transport equation.