Reduced Hausdorff dimension and concentration-cancellation for two-dimensional incompressible flow

Authors:
Ronald J. DiPerna and Andrew Majda

Journal:
J. Amer. Math. Soc. **1** (1988), 59-95

MSC:
Primary 35Q10; Secondary 76C99

DOI:
https://doi.org/10.1090/S0894-0347-1988-0924702-6

MathSciNet review:
924702

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References | Similar Articles | Additional Information

**[1]**R. Adams,*Sobolev spaces*, Academic Press, New York, 1975. MR**0450957 (56:9247)****[2]**R. Adams and N. Meyers,*Bessel potentials. Inclusion relations among classes of exceptional sets*, Indiana Math. J.**22**(1973), 873-905. MR**0320346 (47:8885)****[3]**R. DiPerna and A. Majda,*Oscillations and concentrations in weak solutions of the incompressible fluid equations*, Commun. Math. Phys.**108**(1987), 667-689. MR**877643 (88a:35187)****[4]**-,*Concentrations in regularizations for*-D*incompressible flow*, Comm. Pure Appl. Math.**60**(1987), 301-345. MR**882068 (88e:35149)****[5]**H. Federer and W. P. Ziemer,*The Lebesgue set of a function whose distributional derivatives are pth-power summable*, Indiana Univ. Math. J.**22**(1972), 139-158. MR**0435361 (55:8321)****[6]**P. L. Lions,*The concentration-compactness principle in the calculus of variations: the locally compact case*, Parts I and II, Ann. Inst. H. Poincaré, 1984, 109-145 and 223-283.**[7]**-,*The concentration-compactness principle in the calculus of variations: the limit case*, Parts I and II, Riv. Mat. Iberoamericana I (1984), 145-201 and I (1985), 45-121.**[8]**E. M. Stein,*Singular integrals and differentiability properties of functions*, Princeton University Press, N.J., 1970. MR**0290095 (44:7280)**

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DOI:
https://doi.org/10.1090/S0894-0347-1988-0924702-6

Article copyright:
© Copyright 1988
American Mathematical Society