MASS CONCENTRATION FOR THE L-2-CRITICAL NONLINEAR SCHRODINGER EQUATIONS OF HIGHER ORDERS

作者：Chae Myeongju^*; Hong Sunggeum; Lee Sanghyuk

来源：Discrete and Continuous Dynamical Systems, 2011, 29(3): 909-928.

DOI：10.3934/dcds.2011.29.909

• Schrodinger equations
• high orders
• mixed norm blow-up
• mass concentration

We consider the mass concentration phenomenon for the L-2-critical nonlinear Schrodinger equations of higher orders. We show that any solution u to iu(t) + (-Delta) alpha/2 u - +/-vertical bar u vertical bar 2 alpha/d u, u(0, .) epsilon L-2 for alpha > 2, which blows up in a finite time, satisfies a mass concentration phenomenon near the blow-up time. We verify that as alpha increases, the size of region capturing a mass concentration gets wider due to the stronger dispersive effect.

• 出版日期2011-3-10