메뉴 건너뛰기




Volumn 231, Issue 2, 2012, Pages 1151-1172

Quasilinear Schrödinger equations I: Small data and quadratic interactions

Author keywords

Local existence theory; Schr dinger equations

Indexed keywords


EID: 84864035543     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2012.06.010     Document Type: Article
Times cited : (41)

References (30)
  • 1
    • 33749515447 scopus 로고    scopus 로고
    • Quadratic nonlinear derivative Schrödinger equations. I
    • Bejenaru I. Quadratic nonlinear derivative Schrödinger equations. I. Int. Math. Res. Pap. IMRP 2007, 2006. 84 pp.
    • (2007) Int. Math. Res. Pap. IMRP , vol.2006 , pp. 84
    • Bejenaru, I.1
  • 2
    • 77951160233 scopus 로고    scopus 로고
    • Quadratric nonlinear derivative Schrödinger equations. II
    • Bejenaru I. Quadratric nonlinear derivative Schrödinger equations. II. Trans. Amer. Math. Soc. 2008, 360(11):5925-5957.
    • (2008) Trans. Amer. Math. Soc. , vol.360 , Issue.11 , pp. 5925-5957
    • Bejenaru, I.1
  • 3
    • 56649094234 scopus 로고    scopus 로고
    • Large data local solutions for the derivative NLS equation
    • Bejenaru I., Tataru D. Large data local solutions for the derivative NLS equation. J. Eur. Math. Soc. 2008, 10:957-985.
    • (2008) J. Eur. Math. Soc. , vol.10 , pp. 957-985
    • Bejenaru, I.1    Tataru, D.2
  • 5
    • 0002738813 scopus 로고
    • Local existence for semilinear Schrödinger equations
    • Chihara H. Local existence for semilinear Schrödinger equations. Math. Japon. 1995, 42:35-52.
    • (1995) Math. Japon. , vol.42 , pp. 35-52
    • Chihara, H.1
  • 6
    • 84968508844 scopus 로고
    • Local smoothing properties of dispersive equations
    • Constantin P., Saut J.-C. Local smoothing properties of dispersive equations. J. Amer. Math. Soc. 1989, 1:413-446.
    • (1989) J. Amer. Math. Soc. , vol.1 , pp. 413-446
    • Constantin, P.1    Saut, J.-C.2
  • 7
    • 84990700842 scopus 로고
    • Microlocal dispersive smoothing for the Schrödinger equation
    • Craig W., Kappeler T., Strauss W. Microlocal dispersive smoothing for the Schrödinger equation. Comm. Pure Appl. Math. 1995, 48(8):769-860.
    • (1995) Comm. Pure Appl. Math. , vol.48 , Issue.8 , pp. 769-860
    • Craig, W.1    Kappeler, T.2    Strauss, W.3
  • 8
    • 0039250942 scopus 로고    scopus 로고
    • Smoothing effects for Schrödinger evolution equation and global behavior of geodesic flow
    • Doi S. Smoothing effects for Schrödinger evolution equation and global behavior of geodesic flow. Math. Ann. 2000, 318:355-389.
    • (2000) Math. Ann. , vol.318 , pp. 355-389
    • Doi, S.1
  • 9
    • 84972525950 scopus 로고
    • Remarks on nonlinear Schrödinger equations in one space dimension
    • Hayashi N., Ozawa T. Remarks on nonlinear Schrödinger equations in one space dimension. Differential Integral Equations 1994, 7:453-461.
    • (1994) Differential Integral Equations , vol.7 , pp. 453-461
    • Hayashi, N.1    Ozawa, T.2
  • 10
    • 0003216788 scopus 로고    scopus 로고
    • Lectures on Nonlinear Hyperbolic Differential Equations
    • Berlin
    • L. Hörmander, Lectures on Nonlinear Hyperbolic Differential Equations, in: Mathematiques & Applications, Berlin, 1997.
    • (1997) Mathematiques & Applications
    • Hörmander, L.1
  • 11
    • 84972566457 scopus 로고
    • 2 well-posedness of the Cauchy problem for Schrödinger type equations on a Riemannian manifold and Maslov theory
    • 2 well-posedness of the Cauchy problem for Schrödinger type equations on a Riemannian manifold and Maslov theory. Duke Math. J. 1988, 56:549-588.
    • (1988) Duke Math. J. , vol.56 , pp. 549-588
    • Ichinose, W.1
  • 12
    • 0002362136 scopus 로고
    • On the Cauchy problem for the (generalized) Korteweg-de Vries equation
    • Advances in Math. Supp. Studies
    • Kato T. On the Cauchy problem for the (generalized) Korteweg-de Vries equation. Studies in Applied Math. 1983, vol. 8:93-128.
    • (1983) Studies in Applied Math. , vol.8 , pp. 93-128
    • Kato, T.1
  • 13
    • 33748474667 scopus 로고    scopus 로고
    • The general quasilinear ultrahyperbolic Schrödinger equation
    • Kenig C.E., Ponce G., Rolvung C., Vega L. The general quasilinear ultrahyperbolic Schrödinger equation. Adv. Math. 2005, 196(2):402-433.
    • (2005) Adv. Math. , vol.196 , Issue.2 , pp. 402-433
    • Kenig, C.E.1    Ponce, G.2    Rolvung, C.3    Vega, L.4
  • 14
    • 24044448970 scopus 로고    scopus 로고
    • Variable coefficient Schrödinger flows for ultrahyperbolic operators
    • Kenig C.E., Ponce G., Rolvung C., Vega L. Variable coefficient Schrödinger flows for ultrahyperbolic operators. Adv. Math. 2006, 206(2):373-486.
    • (2006) Adv. Math. , vol.206 , Issue.2 , pp. 373-486
    • Kenig, C.E.1    Ponce, G.2    Rolvung, C.3    Vega, L.4
  • 16
    • 0039165707 scopus 로고    scopus 로고
    • Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations
    • Kenig C.E., Ponce G., Vega L. Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations. Invent. Math. 1998, 134:489-545.
    • (1998) Invent. Math. , vol.134 , pp. 489-545
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 17
    • 7544251725 scopus 로고    scopus 로고
    • The Cauchy problem for quasi-linear Schrödinger equations
    • Kenig C.E., Ponce G., Vega L. The Cauchy problem for quasi-linear Schrödinger equations. Invent. Math. 2004, 158:343-388.
    • (2004) Invent. Math. , vol.158 , pp. 343-388
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 18
    • 84956276540 scopus 로고
    • Generalized solutions to the Cauchy problem for the Korteweg-de Vries equation
    • Krushkov S.N., Faminskii A.V. Generalized solutions to the Cauchy problem for the Korteweg-de Vries equation. Math. U.S.S.R. Sbornik 1984, 48:93-138.
    • (1984) Math. U.S.S.R. Sbornik , vol.48 , pp. 93-138
    • Krushkov, S.N.1    Faminskii, A.V.2
  • 19
    • 0037238971 scopus 로고    scopus 로고
    • On the initial value problem for the one dimensional quasilinear Schrödinger equation
    • Lim W.-K., Ponce G. On the initial value problem for the one dimensional quasilinear Schrödinger equation. SIAM J. Math. Anal. 2003, 34:435-459.
    • (2003) SIAM J. Math. Anal. , vol.34 , pp. 435-459
    • Lim, W.-K.1    Ponce, G.2
  • 20
    • 77951190953 scopus 로고    scopus 로고
    • Introduction to Nonlinear Dispersive Equations
    • Springer, New York
    • Linares F., Ponce G. Introduction to Nonlinear Dispersive Equations. Universitext 2009, Springer, New York.
    • (2009) Universitext
    • Linares, F.1    Ponce, G.2
  • 21
    • 63449104934 scopus 로고    scopus 로고
    • Wave packet parametrices for evolutions governed by PDO's with rough symbols
    • Marzuola J., Metcalfe J., Tataru D. Wave packet parametrices for evolutions governed by PDO's with rough symbols. Proc. Amer. Math. Soc. 2007, 136(2):597-604.
    • (2007) Proc. Amer. Math. Soc. , vol.136 , Issue.2 , pp. 597-604
    • Marzuola, J.1    Metcalfe, J.2    Tataru, D.3
  • 22
    • 0001736587 scopus 로고
    • Some remarks on the Cauchy problem
    • Mizohata S. Some remarks on the Cauchy problem. J. Math. Kyoto Univ. 1961, 1:109-127.
    • (1961) J. Math. Kyoto Univ. , vol.1 , pp. 109-127
    • Mizohata, S.1
  • 25
    • 84864745401 scopus 로고    scopus 로고
    • Ill-posedness for the quadratic D-NLS equation
    • Master's Thesis, University of California at Berkeley
    • T. Schottdorf, Ill-posedness for the quadratic D-NLS equation, Master's Thesis, University of California at Berkeley, 2010.
    • (2010)
    • Schottdorf, T.1
  • 26
    • 0001679726 scopus 로고
    • Regularity of solutions to the Schrödinger equations
    • Sjölin P. Regularity of solutions to the Schrödinger equations. Duke Math. J. 1987, 55:699-715.
    • (1987) Duke Math. J. , vol.55 , pp. 699-715
    • Sjölin, P.1
  • 27
    • 0009035492 scopus 로고
    • Lectures on Nonlinear Wave Equations
    • International Press, Boston
    • Sogge C.D. Lectures on Nonlinear Wave Equations. Monographs in Analysis 1995, vol. II. International Press, Boston.
    • (1995) Monographs in Analysis , vol.2
    • Sogge, C.D.1
  • 28
    • 18144376718 scopus 로고    scopus 로고
    • Rough solutions for the wave maps equation
    • Tataru D. Rough solutions for the wave maps equation. Amer. J. Math. 2005, 127:293-377.
    • (2005) Amer. J. Math. , vol.127 , pp. 293-377
    • Tataru, D.1
  • 30
    • 0000801121 scopus 로고
    • The Schrödinger equation: pointwise convergence to the initial data
    • Vega L. The Schrödinger equation: pointwise convergence to the initial data. Proc. Amer. Math. Soc. 1988, 102:874-878.
    • (1988) Proc. Amer. Math. Soc. , vol.102 , pp. 874-878
    • Vega, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.