TIME-DEPENDENT RESCALINGS AND LYAPUNOV FUNCTIONALS FOR THE VLASOV–POISSON AND EULER–POISSON SYSTEMS, AND FOR RELATED MODELS OF KINETIC EQUATIONS, FLUID DYNAMICS AND QUANTUM PHYSICS
2001 ◽
Vol 11
(03)
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pp. 407-432
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Keyword(s):
We investigate rescaling transformations for the Vlasov–Poisson and Euler–Poisson systems and derive in the plasma physics case Lyapunov functionals which can be used to analyze dispersion effects. The method is also used for studying the long time behavior of the solutions and can be applied to other models in kinetic theory (two-dimensional symmetric Vlasov–Poisson system with an external magnetic field), in fluid dynamics (Euler system for gases) and in quantum physics (Schrödinger–Poisson system, nonlinear Schrödinger equation).
2001 ◽
Vol 30
(2-3)
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pp. 155-168
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1975 ◽
Vol 16
(12)
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pp. 2450-2457
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2011 ◽
Vol 14
(2)
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pp. 279-294
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Keyword(s):
2016 ◽
Vol 15
(5)
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pp. 1743-1756
2017 ◽
Vol 15
(7)
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pp. 1947-1965
2004 ◽
Vol 339
(10)
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pp. 683-688
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Keyword(s):