Hammadi Abidi, Taoufik Hmidi, Sahbi Keraani (2008)
Journées Équations aux dérivées partielles
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This paper deals with the global well-posedness of the D axisymmetric Euler equations for initial data lying in critical Besov spaces . In this case the BKM criterion is not known to be valid and to circumvent this difficulty we use a new decomposition of the vorticity .
Rincon, M.A., Límaco, J., Liu, I-Shih (2006)
Mathematical Physics Electronic Journal [electronic only]
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W. M. Zajączkowski (1995)
Annales Polonici Mathematici
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We prove the local existence of solutions for equations of motion of a viscous compressible barotropic fluid in a domain bounded by a free surface. The solutions are shown to exist in exactly those function spaces where global solutions were found in our previous papers [14, 15].
Ewa Zadrzyńska, Wojciech M. Zajączkowski (1996)
Annales Polonici Mathematici
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We consider the motion of a viscous compressible heat conducting fluid in ℝ³ bounded by a free surface which is under constant exterior pressure. Assuming that the initial velocity is sufficiently small, the initial density and the initial temperature are close to constants, the external force, the heat sources and the heat flow vanish, we prove the existence of global-in-time solutions which satisfy, at any moment of time, the properties prescribed at the initial moment.
Ewa Zadrzyńska, Wojciech M. Zajączkowski (1994)
Annales Polonici Mathematici
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The motion of a viscous compressible heat conducting fluid in a domain in ℝ³ bounded by a free surface is considered. We prove local existence and uniqueness of solutions in Sobolev-Slobodetskiĭ spaces in two cases: with surface tension and without it.
Kordoš, M. (2004)
Acta Mathematica Universitatis Comenianae. New Series
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Carlos E. Kenig (2007)
Journées Équations aux dérivées partielles
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Yoshihiro Shibata (1992)
Banach Center Publications
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The global existence theorem of classical solutions for one-dimensional nonlinear thermoelasticity is proved for small and smooth initial data in the case of a bounded reference configuration for a homogeneous medium, considering the Neumann type boundary conditions: traction free and insulated. Moreover, the asymptotic behaviour of solutions is investigated.
Bui Ton, Grzegorz Łukaszewicz (1992)
Banach Center Publications
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The existence of a weak solution of a non-stationary free boundary transmission problem arising in the production of industrial materials is established. The process is governed by a coupled system involving the Navier--Stokes equations and a non-linear heat equation. The stationary case was studied in [7].