Abstract
We consider a sequencev ε of non-stationary solutions of the incompressible 2D-Euler equation, locally bounded inL 2. We prove that if the defect measure is supported in a one-dimensional set (ℝ3) of some special type (which we call “finite type”), the weak limitv ofv ε is a solution of the Euler equations: our theorem is of the type “concentration-cancellation”.
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Di Perna, R., Majda, A.: Oscillations and concentrations in weak solutions of the incompressible fluid equations. Commun. Math. Phys.108, 667–689 (1987)
Di Perna, R., Majda, A.: Concentrations in regularizations for 2-D incompressible flow. Commun. Pure Appl. Math.40, 301–345 (1987)
Di Perna, R., Majda, A.: Reduced Hausdorff dimension and concentration-cancellation for 2-D incompressible flow. J. Am. Math. Soc.1, 59–95 (1988)
Gerard, P.: Compacité par compensation et régularité 2-microlocale, Séminaire d'EDP (1988–1989), Ecole Polytechnique, Paris, et Article à paraître
Greengard, C., Thomann, E.: On Di Perna-Majda Concentration sets for two-dimensional incompressible flow. Commun. Pure Appl. Math.41, 295–303 (1988)
Lions, P.L.: The concentration-compactness principle in the calculus of variations: The limit case, Part I and Part II. Rev. Mat. Iberoamericana, Vol.1 et2, 145–201 (1985)
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Communicated by A. Jaffe
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Alinhac, S. Un phénomène de concentration évanescente pour des flots non-stationnaires incompressibles en dimension deux. Commun.Math. Phys. 127, 585–596 (1990). https://doi.org/10.1007/BF02104503
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DOI: https://doi.org/10.1007/BF02104503