Frank Merle - Selected Publications#

Kenig, Carlos E.; Merle, Frank: Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case. Invent. Math. 166 (2006), no. 3, 645-675.

Kenig, Carlos E.; Merle, Frank: Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation. Acta Math. 201 (2008), no. 2, 147-212.

Merle, Frank: Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power. Duke Math. J. 69 (1993), no. 2, 427-454.

Merle, Frank; Raphael, Pierre: The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation. Ann. of Math. (2) 161 (2005), no. 1, 157-222.

Merle, Frank; Raphael, Pierre: On universality of blow-up profile for L2 critical nonlinear Schrödinger equation. Invent. Math. 156 (2004), no. 3, 565-672.

Martel, Yvan; Merle, Frank; Tsai, Tai-Peng: Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations. Comm. Math. Phys. 231 (2002), no. 2, 347-373.

Brezis, Haïm; Merle, Frank: Uniform estimates and blow-up behavior for solutions of −Δu=V(x)e^u in two dimensions. Comm. Partial Differential Equations 16 (1991), no. 8-9, 1223-1253.

Merle, Frank; Raphael, Pierre: On a sharp lower bound on the blow-up rate for the L2 critical nonlinear Schrödinger equation. J. Amer. Math. Soc. 19 (2006), no. 1, 37-90.

Matano, Hiroshi; Merle, Frank: On nonexistence of type II blowup for a supercritical nonlinear heat equation. Comm. Pure Appl. Math. 57 (2004), no. 11, 1494-1541.

Martel, Yvan; Merle, Frank: Blow up in finite time and dynamics of blow up solutions for the L2-critical generalized KdV equation. J. Amer. Math. Soc. 15 (2002), no. 3, 617-664.