@article{AIHPC_2000__17_3_371_0, author = {Lopes Filho, Milton C. and Nussenzveig Lopes, Helena J. and Tadmor, Eitan}, title = {Approximate solutions of the incompressible {Euler} equations with no concentrations}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {371--412}, publisher = {Gauthier-Villars}, volume = {17}, number = {3}, year = {2000}, mrnumber = {1771138}, zbl = {0965.35110}, language = {en}, url = {http://archive.numdam.org/item/AIHPC_2000__17_3_371_0/} }
TY - JOUR AU - Lopes Filho, Milton C. AU - Nussenzveig Lopes, Helena J. AU - Tadmor, Eitan TI - Approximate solutions of the incompressible Euler equations with no concentrations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2000 SP - 371 EP - 412 VL - 17 IS - 3 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPC_2000__17_3_371_0/ LA - en ID - AIHPC_2000__17_3_371_0 ER -
%0 Journal Article %A Lopes Filho, Milton C. %A Nussenzveig Lopes, Helena J. %A Tadmor, Eitan %T Approximate solutions of the incompressible Euler equations with no concentrations %J Annales de l'I.H.P. Analyse non linéaire %D 2000 %P 371-412 %V 17 %N 3 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPC_2000__17_3_371_0/ %G en %F AIHPC_2000__17_3_371_0
Lopes Filho, Milton C.; Nussenzveig Lopes, Helena J.; Tadmor, Eitan. Approximate solutions of the incompressible Euler equations with no concentrations. Annales de l'I.H.P. Analyse non linéaire, Volume 17 (2000) no. 3, pp. 371-412. http://archive.numdam.org/item/AIHPC_2000__17_3_371_0/
[1] Sobolev Spaces, Pure and Applied Mathematics, Vol. 65, Academic Press, 1975. | MR | Zbl
,[2] An Introduction to Vortex Methods, Lecture Notes in Math., Vol. 1360, Springer, Berlin, 1968. | MR | Zbl
,[3] A Second-order projection method for the incompressible Navier-Stokes equations, JCP 85 (1989) 257-283. | MR | Zbl
, , ,[4] Intermediate spaces and the class L log+ L, Arkiv Mat. 2 (1973) 215-228. | MR | Zbl
,[5] On Lorentz-Zygmund spaces, Dissert. Math. 175 (1980) 1-72. | MR | Zbl
, ,[6] Interpolation of Operators, Pure and Applied Mathematics, Vol. 129, Academic Press, 1988. | MR | Zbl
, ,[7] A Lagrangian finite element method for the 2-D Euler equations, CPAM 43 (1990) 735-767. | MR | Zbl
, ,[8] Partial regularity of suitable solutions of the Navier-Stokes equations, CPAM 35 (1982) 771-831. | MR | Zbl
, , ,[9] Weak solutions of 2-D Euler equations with initial vorticity in L(log L), J. Differential Equations 103 (1993) 323-337. | MR | Zbl
,[10] Weak solutions of 2-D incompressible Euler equations, Nonlin. Analysis: TMA 23 (1994) 629-638. | MR | Zbl
,[11] The theory of compensated compactness and the system of isentropic gas dynamics, Preprint, MSRI-00527-91, Math. Sci. Res. Inst., Berkeley.
,[12] A numerical method for solving incompressible viscous flow problems, JCP 2 (1967) 12-26. | Zbl
,[13] Onsager's conjecture on the energy conservation for solutions of Euler's equation, Comm. Math. Phys. 165 (1994) 207-209. | MR | Zbl
, ,[14] Wavelets, Acta Numerica 1 (1992) 1-56. | MR | Zbl
, ,[15] Ordinary differential equations Sobolev spaces and transport theory, Invent. Math. 98 (1989) 511-547. | MR | Zbl
, ,[16] Concentrations in regularizations for 2D incompressible flow, Comm. Pure Appl. Math. 40 (1987) 301-345. | MR | Zbl
, ,[ 17] Reduced Hausdorff dimension and concentration-cancelation for 2-D incompressible flow, J. Amer. Math. Soc. 1 (1988) 59-95. | MR | Zbl
, ,[18] Oscillations and concentrations in weak solutions of the incompressible fluid equations, Comm. Math. Phys. 108 (1987) 667-689. | MR | Zbl
, ,[19] Existence de nappes de tourbillon en dimension deux, J. Amer. Math. Soc. 4 (1991) 553-586. | MR | Zbl
,[20] Orlicz-Sobolev spaces and imbedding theorems, J. Funct. Anal. 8 (1971) 52-75. | MR | Zbl
, ,[21] Finite difference schemes for incompressible flows in the velocity impulse density formulation, JCP 130 (1997) 67-76. | MR | Zbl
, ,[22] Navier-Stokes flows in R3 and Morrey spaces, Comm. PDE 14 (1989) 577-618. | MR | Zbl
, ,[23] A forth-order accurate difference approximation for the incompressible Navier-Stokes equations, Comput. Fluids 23 (1994) 575-593. | MR | Zbl
, , ,[24] Second-order convergence of a projection scheme for the incompressible Navier-Stokes equations with boundaries, SINUM 30 (3) (1993) 609-629. | MR | Zbl
, ,[25] A priori temporal regularity for the streamfunction of 2D incompressible, inviscid flow, Nonlinear Analysis Theor. 35 (1999) 871-884. | MR | Zbl
, , , ,[26] Computing vortex sheet motion, in: Proc. Inter. Congress Math. Vol. I, II, Kyoto 1990, Math. Soc. Japan, 1991, pp. 1573-1583. | MR | Zbl
,[27] Non-oscillatory central schemes for the incompressible 2-D Euler equations, Mathematical Research Letters 4 (1997) 1-20. | MR | Zbl
, ,[28] A new proof of Caffarelli-Kohn-Nirenberg's theorem, Preprint. | MR
,[29] Convergence of vortex methods for weak solutions to the 2D Euler equations with vortex sheet data, CPAM 48 (1995) 611-628. | MR | Zbl
, ,[30] Mathematical Topics in Fluid Mechanics, Vol. 1, Incompressible Models, Oxford Lecture Series in Mathematics and its Applications, Vol. 3, Clarendon Press, 1996. | MR | Zbl
,[31] Remarks on weak solutions for vortex sheets with a distinguished sign, Ind. Univ. Math. J. 42 (1993) 921-939. | MR | Zbl
,[32] Wavelets and Operators, Cambridge Studies in Mathematics, Vol. 37, Cambridge Univ. Press, 1992. | MR | Zbl
,[33] 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 (1992) 934-937. | MR | Zbl
,[34] A survey on compensated compactness, in: Cesari L. (Ed.), Contributions to Modern Calculus of Variations, Pitman Research Notes in Mathematics Series, Wiley, New York, 1987, pp. 145-183. | MR
,[35] A refined estimate of the size of concentration sets for 2D incompressible inviscid flow, Ind. Univ. Math. J. 46 (1997) 165-182. | MR | Zbl
,[36] Statistical hydrodynamics, Nuovo Cimento (Supplemento) 6 (1949) 279-287. | MR
,[37] An inviscid flow with compact support in space-time, J. Geom. Anal. 3 (1993) 343-401. | MR | Zbl
,[38] The point-vortex method for periodic weak solutions of the 2-D Euler equations, Comm. Pure Appl. Math. 49 (1996) 911-965. | MR | Zbl
,[39] On the non-uniqueness of weak solution of the Euler equations, Comm. Pure Appl. Math. 50 (1997) 1261-1286. | MR | Zbl
,[40] Compensated compactness and applications to partial differential equations, in: Nonlinear Analysis and Mechanics, Heriot-Watt Symposium, IV, Pitman, London, 1979. | MR | Zbl
,[41] Navier-Stokes Equations, North-Holland, Amsterdam, 1977. | MR | Zbl
,[42] Gradient estimation on Navier-Stokes equations, Preprint. | MR
, ,[43] On imbeddings into Orlicz spaces and some applications, J. Math. and Mechanics 17 (1967) 473-483. | MR | Zbl
,[44] On L1-vorticity for 2-D incompressible flow, Manuscripta Math. 78 (1993) 403-412. | MR | Zbl
, ,[45] Hydrodynamics in Besov spaces, Anch. Rat. Mech. Anal. 145 (1998) 197-214. | MR | Zbl
,[46] Incompressible flows of an ideal fluid with vorticity in borderline spaces of Besov type, Ann. Sci. Ecole Norm. Sup. 32 (1999) 769-812. | Numdam | MR | Zbl
,[47] Non-stationary flow of an ideal incompressible liquid, USSR Comp. Math. and Math. Phys. 3 (1963) 1407-1456. English transl. | Zbl
,[48] Uniqueness theorem for the basic nonstationary problem in the dynamics of an ideal incompressible fluid, Math. Res. Letters 2 (1995) 27-38. | MR | Zbl
,[49] Weakly Differentiable Functions, Graduate Texts in Mathematics, Vol. 120, Springer, 1989. | MR | Zbl
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