L. Farah

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20082026

most citedLocal solutions in Sobolev spaces with negative indices for the "good" Boussinesq equation

91 citations · 311 across the 34 of their papers we have counts for

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math.AP2026

Threshold solutions for the $3 d$ cubic INLS: the energy-critical case

Luccas Campos, Luiz Gustavo Farah, Jason Murphy

We study the energy-critical $3 d$ cubic inhomogeneous NLS equation $i \partial_{t} u + Δ u + ∣ x ∣^{- 1} ∣ u ∣^{2} u = 0$ . In this work, we prove the existence of special solutions $W^{\pm}$ with…

math.AP2026

Threshold solutions for the $3 d$ cubic INLS: the energy-subcritical case

Luccas Campos, Luiz Gustavo Farah, Jason Murphy

We revisit the work [L. Campos and J. Murphy, SIAM J. Math. Anal., 55 (2023), pp. 3807--3843], which classified the dynamics of $H^{1}$ solutions at the ground state threshold for cu…

Threshold solutions for the 3d cubic INLS: the energy-critical case

Threshold solutions for the 3d cubic INLS: the energy-subcritical case

Threshold solutions for the $3 d$ cubic INLS: the energy-critical case

Threshold solutions for the $3 d$ cubic INLS: the energy-subcritical case