On a new scale of regularity spaces with applications to Euler's equations

Nonlinearity

Volumn 14, Issue 3, 2001, Pages 513-532

  Tadmor, Eitan ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035343982     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/14/3/305     Document Type: Article

References (28)

1. Bennett C and Rudnick K 1980 On Lorentz-Zygmund spaces Dissert. Math. 175 1-72
2. Bennett C and Sharpley R 1988 Interpolation of Operators (Pure and Applied Mathematics vol 129) (New York: Academic)
3. Chae D 1994 Weak solutions of 2-D incompressible Euler equations Nonlin. Analysis TMA 23 629-38
4. Chorin A 1998 Vorticity and Turbulence (Applied Mathematical Sciences vol 103) (Berlin: Springer)
5. Constantin P and Fefferman Ch 1993 Ind. Univ. Math. J. 42 775-89
6. Daubechies I 1992 Ten Lectures on Wavelets (CBMS-NSF Series in Applied Mathematics) (Philadelphia, PA: SIAM)
7. DeVore R Private communication
8. DeVore R, Jawerth B and Popov V 1992 Compression of wavelets decompositions J. AMS 114 737-85
9. DeVore R and Lorentz G G 1991 Constructive Approximation vol 303 (Berlin: Springer)
10. DeVore R and Lucier B 1992 Wavelets Acta Numerica 1 1-56
11. DiPerna R and Majda A 1987 Concentrations in regularizations for 2D incompressible flow Commun. Pure Appl. Math. XL 301-45
12. DiPerna R and Majda A 1988 Reduced Hausdorff dimension and concentration-cancelation for 2-D incompressible flow J. Am. Math. Soc. 1 59-95
13. DiPerna R and Majda A 1987 Oscillations and concentrations in weak solutions of the incompressible fluid equations Commun. Math. Phys. 108 667-89
14. Delort J-M 1991 Existence de nappes de tourbillon en dimension deux J. Am. Math. Soc. 4 553-86
15. 3 and Morrey spaces Commun. PDE 14 577-618
16. Gilbarg D and Trudinger D 1997 Elliptic Partial Differential Equations of Second Order (Berlin: Springer)
17. Greengard C and Thomann E 1988 On DiPerna-Majda concentration sets for two-dimensional incompressible flow Commun. Pure Appl. Math. XLI 295-303
18. Hounie J, Lopes Filho M C, Nussenzveig Lopes H J and Schochet S 1997 A priori temporal regularity for the streamfunction of 2D incompressible, inviscid flow Nonlinear Anal. TMA 8 5053-58
19. Leib E and Loss M 1996 Analysis (Graduate Studies in Mathematics) (Providence, RI: American Mathematical Society)
20. Lions P L 1996 Mathematical Topics in Fluid Mechanics, vol 1, Incompressible Models (Oxford Lecture Series in Mathematics and its Applications vol 3) (Oxford: Clarendon)
21. Lopes Filho M C, Nussenzveig Lopes H J and Tadmor E 2001 Approximate solution of the incompressible Euler equations with no concentrations Ann. Insitut H Poincaré C 17 371-412
22. Majda A 1993 Remarks on weak solutions for vortex sheets with a distinguished sign Ind. Univ. Math. J. 42 921-39
23. Meyer Y 1992 Wavelets and Operators (Cambridge Studies in Mathematics vol 37) (Cambridge: Cambridge University Press)
24. Morgulis A B 1992 On existence of two-dimensional nonstationary flows of an ideal incompressible liquid admitting a curl nonsummable to any power greater than 1 Siberian Math. J. 33 934-7
25. Murat F 1987 A survey on compensated compactness Contributions to Modern Calculus of Variations (Pitman Research Notes in Mathematics Series) ed L Cesari (New York: Wiley) pp 145-83
26. Nussenzveig Lopes H J 1997 A refined estimate of the size of concentration sets for 2D incompressible inviscid flow Ind. Univ. Math. J. 46 165-82
27. Schochet S 1995 The weak vorticity formulation of the 2D Euler equations and concentration-cancellation Commun. PDEs 20 1077-104
28. Stein E 1993 Harmonic Analysis (Princeton, NJ: Princeton University Press)