On well-posedness for some dispersive perturbations of Burgers' equation
Tài liệu tham khảo
Angulo
Arnesen, 2016, Existence of solitary-wave solutions to nonlocal equations, Discrete Contin. Dyn. Syst., 36, 3483, 10.3934/dcds.2016.36.3483
Bernicot, 2009, Uniform estimates for paraproducts and related multilinear multipliers, Rev. Mat. Iberoam., 25, 1055, 10.4171/RMI/589
Bona, 1975, The initial value problem for the Korteweg–de Vries equation, Philos. Trans. R. Soc. Lond. Ser. A, 278, 555, 10.1098/rsta.1975.0035
Bourgain, 1993, Fourier transform restriction phenomena for certain lattice subsets and application to nonlinear evolution equations I. The Schrödinger equation, Geom. Funct. Anal., 3, 157, 10.1007/BF01896021
Burq, 2008, On well-posedness for the Benjamin–Ono equation, Math. Ann., 340, 497, 10.1007/s00208-007-0150-y
Christ, 2001, Maximal functions associated to filtrations, J. Funct. Anal., 179, 409, 10.1006/jfan.2000.3687
Coifman, 1978, Au delà des opérateurs pseudo-différentiels, vol. 57
Colliander, 2003, Sharp global well-posedness for KdV and modified KdV on R and T, J. Am. Math. Soc., 16, 705, 10.1090/S0894-0347-03-00421-1
Fonseca, 2013, The IVP for the dispersion generalized Benjamin–Ono equation in weighted Sobolev spaces, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 30, 763, 10.1016/j.anihpc.2012.06.006
Ginibre, 1995, Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d'espace (d'après Bourgain), Astérisque, 237, 163
Guo, 2012, Local well-posedness for dispersion generalized Benjamin–Ono equations in Sobolev spaces, J. Differ. Equ., 252, 2053, 10.1016/j.jde.2011.10.012
Herr, 2010, A para-differential renormalization technique for nonlinear dispersive equations, Commun. Partial Differ. Equ., 35, 1827, 10.1080/03605302.2010.487232
Ifrim
Ionescu, 2007, Global well-posedness of the Benjamin–Ono equation in low-regularity spaces, J. Am. Math. Soc., 20, 753, 10.1090/S0894-0347-06-00551-0
Ionescu, 2008, Global well-posedness of the KP-I initial value problem in the energy space, Invent. Math., 173, 265, 10.1007/s00222-008-0115-0
Kenig, 2003, On the local well-posedness of the Benjamin–Ono and modified Benjamin–Ono equations, Math. Res. Lett., 10, 879, 10.4310/MRL.2003.v10.n6.a13
Kenig, 1991, Oscillatory integrals and regularity of dispersive equations, Indiana Univ. Math. J., 40, 33, 10.1512/iumj.1991.40.40003
Kenig, 1993, Well-posedness and scattering results for the generalized Korteweg–de Vries equation via the contraction principle, Commun. Pure Appl. Math., 46, 527, 10.1002/cpa.3160460405
Klein, 2015, A numerical approach to blow-up issues for dispersive perturbations of Burgers' equation, Physica D, 295–296, 46, 10.1016/j.physd.2014.12.004
Koch, 2003, On the local well-posedness of the Benjamin–Ono equation in Hs(R), Int. Math. Res. Not., 26, 1449, 10.1155/S1073792803211260
Linares, 2014, Dispersive perturbations of Burgers and hyperbolic equations I: local theory, SIAM J. Math. Anal., 46, 1505, 10.1137/130912001
Linares, 2015, Remarks on the orbital stability of ground state solutions of fKdV e relative equations, Adv. Differ. Equ., 20, 835
Lions, 1972, Non-Homogeneous Boundary Value Problems and Applications, vol. I, vol. 181
Molinet, 2001, Ill-posedness issues for the Benjamin–Ono and related equations, SIAM J. Math. Anal., 33, 982, 10.1137/S0036141001385307
Molinet, 2012, The Cauchy problem for the Benjamin–Ono equation in L2 revisited, Anal. PDE, 5, 365, 10.2140/apde.2012.5.365
Molinet
Molinet
Molinet, 2015, Improvement of the energy method for strongly non resonant dispersive equations and applications, Anal. PDE, 8, 1455, 10.2140/apde.2015.8.1455
Muscalu, 2004, Bi-parameter paraproducts, Acta Math., 193, 269, 10.1007/BF02392566
Ponce, 1991, On the global well-posedness of the Benjamin–Ono equation, Differ. Integral Equ., 4, 527
Saut, 1979, Sur quelques généralisations de l'équation de KdV, J. Math. Pures Appl., 58, 21
Smith, 2000, Global Strichartz estimates for nontrapping perturbations of the Laplacian, Commun. Partial Differ. Equ., 25, 2171, 10.1080/03605300008821581
Tao, 2004, Global well-posedness of the Benjamin–Ono equation in H1(R), J. Hyperbolic Differ. Equ., 1, 27, 10.1142/S0219891604000032