Sunto
Si considera un problema di frontiera libera per l’equazione del moto unidimensionale isoentropico con viscosità dipendente dalla densità secondo la legge μ =b ϱ β, doveb e β sono costanti positive. Si dimostra che esiste un’unica soluzione debole globale nel tempo, purché β<1/3.
Abstract
We consider a free boundary problem for the equation of the one-dimensional isentropic motion with density-dependent viscosity μ =b ϱ β, whereb and β are positive constants. We prove that there exists an unique weak solution globally in time, provided that β<1/3.
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References
M. Okada,Free boundary value problems for the equation of one-dimensionals motion of viscous gas, Japan J. Indust. Appl. Math.,6 (1989), pp. 161–177.
R. Balian,From microphysics to macrophysics, Texts and monographs in physics, Springer (1982).
H. Grad,Asymptotic theory of the Boltzmann equation. II. In: Rarefied gas dynamics, 1 (ed. J. Laurmann), New York Academic Press (1963), pp. 26–59.
S. Kawashima —A. Matsumura —T. Nishida,On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation, Commun. Math. Phys.,70 (1979), pp. 97–124.
S. Jiang,Global smooth solutions of the equations of a viscous, heat-conducting, one-dimensional gas with density-dependent viscosity, Math. Nachr.,190 (1998), pp. 169–183.
Š. Matušů-Nečasová —M. Okada —T. Makino,Free boundary problem for the equation of spherically symmetric motion of viscous gas (II), Japan J. Indust. Appl. Math.,12 (1995), pp. 195–203.
P. L. Lions,Mathematical topics in fluid dynamics, Vol. 2, Compressible models, Oxford Science Publication, Oxford.
E. Feireisl— H. Petzeltová,On the integrability up to the boundary of the weak solutions of the Navier-Stokes equations of compressible flow, Preprint ’99.
E. Feireisl—Š. Matušů-Nečasová—H. Petzeltová—I. Straškraba,On the motion of a viscous compressible flow driven by a time-periodic external force, accepted by ARMA.
M. Padula,Existence and continuous dependence for solutions to the equations of a one-dimensional model in gas-dynamics, Mecanica J. of the A.I.ME.T.A.,17 (1981), p. 128.
M. Padula—H. F. Yashima—A. Novotný,Existence of global solutions to one-dimensional flow of a compressible heat-conducting fluid having general initial densities, Ricerche Math.,42 (1993), pp. 199–248.
V. A. Vaigant—A. V. Kazhikov,On the existence of global solutions to the two-dimensional Navier-Stokes equations for a compressible viscous fluid, Sib. Math. J.,36 (1995), pp. 1108–1141 in Russian translated to Sib. Math. Zh.,36, No. 6, pp. 1283–1316.
T. Yang— Z. Yao— C. Zhu,Compressible Navier-Stokes equations with density-dependent viscosity and vacuum, preprint, 1999.
S. Jiang— Z. Xin— P. Zhang,Global weak solutions to 1D compressible isentropic Navier-Stokes equations with density-dependent viscosity, preprint, 1999.
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Okada, M., Matušů-Nečasová, Š. & Makino, T. Free boundary problem for the equation of one-dimensional motion of compressible gas with density-dependent viscosity. Ann. Univ. Ferrara 48, 1–20 (2002). https://doi.org/10.1007/BF02824736
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DOI: https://doi.org/10.1007/BF02824736