Acta mathematica scientia,Series B ›› 2013, Vol. 33 ›› Issue (6): 1522-1530.doi: 10.1016/S0252-9602(13)60101-0

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ON A CLASS OF INHOMOGENEOUS, ENERGY-CRITICAL, FOCUSING, NONLINEAR SCHRÖDINGER EQUATIONS

 LIU Zhao-Xia   

  1. Department of Information and Computational Science, School of Sciences, Minzu University of China, Beijing 100081, China
  • Received:2012-08-20 Online:2013-11-20 Published:2013-11-20
  • Supported by:

    Supported by NSF of China (11101450, 11071239).

Abstract:

In this paper, we study the Cauchy problem of the inhomogeneous energycritical Schr¨odinger equation: i∂tu = −Δuk(x)|u| 4/N−2 u, N ≥3. Using the potential well method, we establish some new sharp criteria for blow-up of solutions in the nonradial case. In particular, our conclusion in some sense improves on the results in [Kenig and Merle, Invent. Math. 166, 645-675 (2006)], where only the radial case is considered in dimensions 3, 4, 5.

Key words: focusing Schr¨odinger equation, critical energy

CLC Number: 

  • 35Q40
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