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Nonlinear evolution equations and the Euler flow. (English) Zbl 0545.76007
Summary: A new theorem on abstract nonlinear equations of evolution is proved. As an application, the existence, uniqueness, regularity, and continuous dependence on the data are proved for the solution of the Euler equation for incompressible fluids in a bounded domain in \(R^ m\).

76Bxx Incompressible inviscid fluids
Full Text: DOI
[1] Ebin, D.G; Marsden, J, Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of math., 92, 102-163, (1970) · Zbl 0211.57401
[2] Bourguignon, J.P; Brezis, H, Remarks on the Euler equation, J. funct. anal., 15, 341-363, (1974) · Zbl 0279.58005
[3] Temam, R, On the Euler equations of incompressible perfect fluids, J. funct. anal., 20, 32-43, (1975) · Zbl 0309.35061
[4] Temam, R, Local existence of C∞ solutions of the Euler equations of incompressible perfect fluids, (), 184-194
[5] Lai, C.Y, Studies on the Euler and the Navier-Stokes equations, ()
[6] Bardos, C; Frisch, U, Finite-time regularity for bounded and unbounded ideal incompressible fluids using holder estimates, (), 1-13 · Zbl 0355.76016
[7] Foias, C; Frisch, U; Temam, R, Existence de solutions C∞ des equations d’Euler, C. R. acad. sci. Paris, ser. A, 280, 505-508, (1975) · Zbl 0309.35015
[8] Kato, T, Quasi-linear equations of evolution, with applications to partial differential equations, (), 25-70
[9] Kato, T, Quasi-linear equations of evolution in nonreflexive Banach spaces, (), to appear · Zbl 0532.35048
[10] Nakata, M, Quasi-linear evolution equations in non-reflexive Banach spaces and applications to hyperbolic systems, ()
[11] Nirenberg, L, Remarks on strongly elliptic partial differential equations, Comm. pure appl. math., 8, 649-675, (1955) · Zbl 0067.07602
[12] Lions, J.L; Magenes, E, Problèmes aux limites non homogènes, Ann. inst. Fourier (Grenoble), 11, 137-178, (1961) · Zbl 0101.07901
[13] Bona, J.L; Smith, R, The initial-value problem for the Korteweg-de Vries equation, Philos. trans. roy. soc. London, A278, 555-601, (1975) · Zbl 0306.35027
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