Tohoku Mathematical Journal
2023
June
SECOND SERIES VOL. 75, NO. 2

Tohoku Math. J.
75 (2023), 215-232

Title MINIMAL MASS BLOW-UP SOLUTIONS FOR NONLINEAR SCHRÖDINGER EQUATIONS WITH A POTENTIAL

Author Naoki Matsui

(Received March 22, 2021, revised December 9, 2021)
Abstract. We consider a mass critical nonlinear Schrödinger equation with a real-valued potential. In this work, we construct a minimal mass solution that blows up at finite time, under weaker assumptions on spatial dimensions and potentials than Banica, Carles, and Duyckaerts (2011). Moreover, we show that the blow-up solution converges to a blow-up profile. Furthermore, we improve some parts of the arguments in Raphaël and Szeftel (2011) and Le Coz, Martel, and Raphaël (2016).

Mathematics Subject Classification. Primary 35Q55.
Key words and phrases. Blow-up, critical mass, minimal mass, nonlinear Schrödinger equation, potential.

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