Bégout, Pascal and Vargas, Ana (2007) Mass Concentration Phenomena for the L^2-Critical Nonlinear Schrödinger Equation. Transactions of the American Mathematical Society (TRAN), 359 (11). pp. 5257-5282.

Preview

Text Download (556kB) | Preview

Abstract

In this paper, we show that any solution of the nonlinear Schrödinger equation $iu_t+\Delta u\pm|u|^\frac{4}{N}u=0,$ which blows up in finite time, satisfies a mass concentration phenomena near the blow-up time. Our proof is essentially based on the Bourgain's one [3], which has established this result in the bidimensional spatial case, and on a generalization of Strichartz's inequality, where the bidimensional spatial case was proved by Moyua, Vargas and Vega [17]. We also generalize to higher dimensions the results in Keraani [13] and Merle and Vega [15].