LEADER 01043nam a2200289 i 4500 001 991001114999707536 005 20020507183533.0 008 980129s1972 us ||| | eng 020 $a0135616964 035 $ab10802988-39ule_inst 035 $aLE01307256$9ExL 040 $aDip.to Matematica$beng 082 0 $a006.35 084 $aAMS 68S05 100 1 $aGross, Maurice$047417 245 10$aMathematical models in linguistics /$cMaurice Gross 260 $aEnglewood Cliffs, N. J. :$bPrentice-Hall,$cc1972 300 $axvi, 159 p. :$bill. ;$c24 cm. 490 0 $aPrentice-Hall foundations of modern linguistics series 500 $aBibliography: p. 155-156 650 4$aMathematical linguistics 907 $a.b10802988$b23-02-17$c28-06-02 912 $a991001114999707536 945 $aLE013 68S05 GRO11 (1972)$g1$i2013000094670$lle013$o-$pE0.00$q-$rl$s- $t0$u0$v0$w0$x0$y.i10907336$z28-06-02 996 $aMathematical models in linguistics$923652 997 $aUNISALENTO 998 $ale013$b01-01-98$cm$da $e-$feng$gus $h0$i1 LEADER 03890nam 22006015 450 001 9910300106603321 005 20251216184505.0 010 $a3-319-99486-7 024 7 $a10.1007/978-3-319-99486-4 035 $a(CKB)4100000007110540 035 $a(MiAaPQ)EBC5588731 035 $a(DE-He213)978-3-319-99486-4 035 $a(PPN)232471592 035 $a(EXLCZ)994100000007110540 100 $a20181102d2018 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAlmost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle /$fby Massimiliano Berti, Jean-Marc Delort 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (276 pages) 225 1 $aLecture Notes of the Unione Matematica Italiana,$x1862-9113 ;$v24 311 08$a3-319-99485-9 330 $aThe goal of this monograph is to prove that any solution of the Cauchy problem for the capillary-gravity water waves equations, in one space dimension, with periodic, even in space, small and smooth enough initial data, is almost globally defined in time on Sobolev spaces, provided the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, a normal forms-based procedure is used, eliminating those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations form a quasi-linear system, the usual normal forms approaches would face the well-known problem of losses of derivatives in the unbounded transformations. To overcome this, after a paralinearization of the capillary-gravity water waves equations, we perform several paradifferential reductions to obtain a diagonal system with constant coefficient symbols, up to smoothing remainders. Then we start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization. The reversible structure of the water waves equations, and the fact that we seek solutions even in space, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions. 410 0$aLecture Notes of the Unione Matematica Italiana,$x1862-9113 ;$v24 606 $aDifferential equations, Partial 606 $aFourier analysis 606 $aDynamics 606 $aErgodic theory 606 $aFunctional analysis 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aFourier Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12058 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 615 0$aDifferential equations, Partial. 615 0$aFourier analysis. 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aFunctional analysis. 615 14$aPartial Differential Equations. 615 24$aFourier Analysis. 615 24$aDynamical Systems and Ergodic Theory. 615 24$aFunctional Analysis. 676 $a515.3534 700 $aBerti$b Massimiliano$4aut$4http://id.loc.gov/vocabulary/relators/aut$0309729 702 $aDelort$b Jean-Marc$f1961-$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910300106603321 996 $aAlmost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle$92182077 997 $aUNINA