Cordoba, Diego; Fefferman, Charles Behavior of several two-dimensional fluid equations in singular scenarios. (English) Zbl 0965.35133 Proc. Natl. Acad. Sci. USA 98, No. 8, 4311-4312 (2001). Summary: We give conditions that rule out formation of sharp fronts for certain two-dimensional incompressible flows. We show that a necessary condition of having a sharp front is that the flow has to have uncontrolled velocity growth. In the case of the quasi-geostrophic equation and two-dimensional Euler equation, we obtain estimates on the formation of semi-uniform fronts. Cited in 19 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 80A20 Heat and mass transfer, heat flow (MSC2010) 35Q05 Euler-Poisson-Darboux equations Keywords:quasi-geostrophic equation; two-dimensional Euler equation; formation of semi-uniform fronts PDFBibTeX XMLCite \textit{D. Cordoba} and \textit{C. Fefferman}, Proc. Natl. Acad. Sci. USA 98, No. 8, 4311--4312 (2001; Zbl 0965.35133) Full Text: DOI References: [1] COMMUN MATH PHYS 94 pp 61– (1984) · Zbl 0573.76029 · doi:10.1007/BF01212349 [2] 7 pp 1495– (1994) · Zbl 0809.35057 · doi:10.1088/0951-7715/7/6/001 [3] COMMUN MATH PHYS 184 pp 443– (1997) · Zbl 0874.76092 · doi:10.1007/s002200050067 [4] 1 pp 49– (1994) [5] COMMUN PART DIFF EQ 21 pp 559– (1996) · Zbl 0853.35091 · doi:10.1080/03605309608821197 [6] PHYS FLUIDS A 4 pp 1472– (1992) · Zbl 0825.76121 · doi:10.1063/1.858422 [7] PHILOS TRANS R SOC LONDON A 351 pp 1– (1995) · Zbl 0829.76098 · doi:10.1098/rsta.1995.0024 [8] J COMPUT PHYS 134 pp 190– (1997) · Zbl 0879.76079 · doi:10.1006/jcph.1997.5683 [9] COMMUN PURE APPL MATH 53 pp 512– (2000) · Zbl 1038.76060 · doi:10.1002/(SICI)1097-0312(200004)53:4<512::AID-CPA4>3.0.CO;2-R [10] 9 pp 876– (1997) · Zbl 1185.76841 · doi:10.1063/1.869184 [11] ANN MATH 148 pp 1135– (1998) · Zbl 0920.35109 · doi:10.2307/121037 [12] PHYS LETT A 241 pp 168– (1998) · Zbl 0974.76512 · doi:10.1016/S0375-9601(98)00108-X This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.