Duyckaerts, Thomas; Kenig, Carlos; Martel, Yvan; Merle, Frank Soliton resolution for critical co-rotational wave maps and radial cubic wave equation. (English) Zbl 1491.35292 Commun. Math. Phys. 391, No. 2, 779-871 (2022). Reviewer: Dongbing Zha (Shanghai) MSC: 35L71 35B40 35B44 35L15 35Q55 PDFBibTeX XMLCite \textit{T. Duyckaerts} et al., Commun. Math. Phys. 391, No. 2, 779--871 (2022; Zbl 1491.35292) Full Text: DOI arXiv
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor; Szeftel, Jeremie On blow up for the energy super critical defocusing nonlinear Schrödinger equations. (English) Zbl 1487.35353 Invent. Math. 227, No. 1, 247-413 (2022). MSC: 35Q55 35Q31 76N10 35B44 35D35 35C06 PDFBibTeX XMLCite \textit{F. Merle} et al., Invent. Math. 227, No. 1, 247--413 (2022; Zbl 1487.35353) Full Text: DOI arXiv
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank Decay estimates for nonradiative solutions of the energy-critical focusing wave equation. (English) Zbl 1472.35050 J. Geom. Anal. 31, No. 7, 7036-7074 (2021). MSC: 35B40 35C08 35L15 35L71 PDFBibTeX XMLCite \textit{T. Duyckaerts} et al., J. Geom. Anal. 31, No. 7, 7036--7074 (2021; Zbl 1472.35050) Full Text: DOI arXiv
Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank Scattering profile for global solutions of the energy-critical wave equation. (English) Zbl 1437.35497 J. Eur. Math. Soc. (JEMS) 21, No. 7, 2117-2162 (2019). MSC: 35L71 35L15 35B33 35B40 PDFBibTeX XMLCite \textit{T. Duyckaerts} et al., J. Eur. Math. Soc. (JEMS) 21, No. 7, 2117--2162 (2019; Zbl 1437.35497) Full Text: DOI arXiv
Merle, Frank; Zaag, Hatem Solution to the semilinear wave equation with a pyramid-shaped blow-up surface. (English) Zbl 1475.35209 Sémin. Laurent Schwartz, EDP Appl. 2016-2017, Exp. No. 6, 13 p. (2017). MSC: 35L71 35B40 35B44 35C08 35L15 35L05 35L67 PDFBibTeX XMLCite \textit{F. Merle} and \textit{H. Zaag}, Sémin. Laurent Schwartz, EDP Appl. 2016--2017, Exp. No. 6, 13 p. (2017; Zbl 1475.35209) Full Text: DOI Numdam
Martel, Yvan; Merle, Frank Construction of multi-solitons for the energy-critical wave equation in dimension 5. (English) Zbl 1359.35166 Arch. Ration. Mech. Anal. 222, No. 3, 1113-1160 (2016). Reviewer: Boris A. Malomed (Tel Aviv) MSC: 35Q51 35C08 35C07 PDFBibTeX XMLCite \textit{Y. Martel} and \textit{F. Merle}, Arch. Ration. Mech. Anal. 222, No. 3, 1113--1160 (2016; Zbl 1359.35166) Full Text: DOI arXiv
Merle, Frank; Zaag, Hatem Dynamics near explicit stationary solutions in similarity variables for solutions of a semilinear wave equation in higher dimensions. (English) Zbl 1339.35062 Trans. Am. Math. Soc. 368, No. 1, 27-87 (2016). MSC: 35B44 35L71 35L67 35B40 PDFBibTeX XMLCite \textit{F. Merle} and \textit{H. Zaag}, Trans. Am. Math. Soc. 368, No. 1, 27--87 (2016; Zbl 1339.35062) Full Text: DOI arXiv
Merle, Frank; Zaag, Hatem On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations. (English) Zbl 1315.35134 Commun. Math. Phys. 333, No. 3, 1529-1562 (2015). Reviewer: Chengbo Wang (Hangzhou) MSC: 35L71 35B44 PDFBibTeX XMLCite \textit{F. Merle} and \textit{H. Zaag}, Commun. Math. Phys. 333, No. 3, 1529--1562 (2015; Zbl 1315.35134) Full Text: DOI arXiv
Merle, Frank; Zaag, Hatem Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation. (English) Zbl 1270.35320 Duke Math. J. 161, No. 15, 2837-2908 (2012). Reviewer: Satyanad Kichenassamy (Reims) MSC: 35L71 35B44 PDFBibTeX XMLCite \textit{F. Merle} and \textit{H. Zaag}, Duke Math. J. 161, No. 15, 2837--2908 (2012; Zbl 1270.35320) Full Text: DOI arXiv Euclid
Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case. (English) Zbl 1282.35088 J. Eur. Math. Soc. (JEMS) 14, No. 5, 1389-1454 (2012). Reviewer: Marcelo M. Cavalcanti (Maringá) MSC: 35B44 35L71 35B33 PDFBibTeX XMLCite \textit{T. Duyckaerts} et al., J. Eur. Math. Soc. (JEMS) 14, No. 5, 1389--1454 (2012; Zbl 1282.35088) Full Text: DOI arXiv
Merle, Frank; Zaag, Hatem Blow-up behavior outside the origin for a semilinear wave equation in the radial case. (English) Zbl 1222.35126 Bull. Sci. Math. 135, No. 4, 353-373 (2011). Reviewer: Marie Kopáčková (Praha) MSC: 35L71 35L05 35B44 35B40 35L67 PDFBibTeX XMLCite \textit{F. Merle} and \textit{H. Zaag}, Bull. Sci. Math. 135, No. 4, 353--373 (2011; Zbl 1222.35126) Full Text: DOI arXiv
Martel, Yvan; Merle, Frank Inelastic interaction of nearly equal solitons for the quartic gKdV equation. (English) Zbl 1230.35121 Invent. Math. 183, No. 3, 563-648 (2011). Reviewer: Pilar Ruiz Gordoa (Madrid) MSC: 35Q53 35Q51 PDFBibTeX XMLCite \textit{Y. Martel} and \textit{F. Merle}, Invent. Math. 183, No. 3, 563--648 (2011; Zbl 1230.35121) Full Text: DOI arXiv
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank Universality of blow-up profile for small radial type II blow-up solutions of the energy-critical wave equation. (English) Zbl 1230.35067 J. Eur. Math. Soc. (JEMS) 13, No. 3, 533-599 (2011). Reviewer: Pavol Quittner (Bratislava) MSC: 35L71 35B44 PDFBibTeX XMLCite \textit{T. Duyckaerts} et al., J. Eur. Math. Soc. (JEMS) 13, No. 3, 533--599 (2011; Zbl 1230.35067) Full Text: DOI arXiv
Martel, Yvan; Merle, Frank Stability of two soliton collision for nonintegrable gKdV equations. (English) Zbl 1179.35291 Commun. Math. Phys. 286, No. 1, 39-79 (2009). MSC: 35Q53 35Q51 35B35 37K40 35C08 PDFBibTeX XMLCite \textit{Y. Martel} and \textit{F. Merle}, Commun. Math. Phys. 286, No. 1, 39--79 (2009; Zbl 1179.35291) Full Text: DOI arXiv
Kenig, Carlos E.; Merle, Frank Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation. (English) Zbl 1183.35202 Acta Math. 201, No. 2, 147-212 (2008). Reviewer: Marie Kopáčková (Praha) MSC: 35L71 35L15 35B44 35A01 PDFBibTeX XMLCite \textit{C. E. Kenig} and \textit{F. Merle}, Acta Math. 201, No. 2, 147--212 (2008; Zbl 1183.35202) Full Text: DOI arXiv
Merle, Frank; Zaag, Hatem Openness of the set of non-characteristic points and regularity of the blow-up curve for the 1 D semilinear wave equation. (English) Zbl 1159.35046 Commun. Math. Phys. 282, No. 1, 55-86 (2008). Reviewer: Marie Kopáčková (Praha) MSC: 35L70 35B40 35L15 PDFBibTeX XMLCite \textit{F. Merle} and \textit{H. Zaag}, Commun. Math. Phys. 282, No. 1, 55--86 (2008; Zbl 1159.35046) Full Text: DOI
Martel, Yvan; Merle, Frank Asymptotic stability of solitons of the gKdV equations with general nonlinearity. (English) Zbl 1153.35068 Math. Ann. 341, No. 2, 391-427 (2008). MSC: 35Q53 35Q51 35B40 PDFBibTeX XMLCite \textit{Y. Martel} and \textit{F. Merle}, Math. Ann. 341, No. 2, 391--427 (2008; Zbl 1153.35068) Full Text: DOI arXiv
Merle, Frank; Zaag, Hatem Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension. (English) Zbl 1133.35070 J. Funct. Anal. 253, No. 1, 43-121 (2007). Reviewer: Marie Kopáčková (Praha) MSC: 35L70 35L15 35B40 PDFBibTeX XMLCite \textit{F. Merle} and \textit{H. Zaag}, J. Funct. Anal. 253, No. 1, 43--121 (2007; Zbl 1133.35070) Full Text: DOI
Martel, Yvan; Merle, Frank; Tsai, Tai-Peng Stability in \(H^1\) of the sum of \(K\) solitary waves for some nonlinear Schrödinger equations. (English) Zbl 1099.35134 Duke Math. J. 133, No. 3, 405-466 (2006). MSC: 35Q55 37K45 35Q51 35B35 PDFBibTeX XMLCite \textit{Y. Martel} et al., Duke Math. J. 133, No. 3, 405--466 (2006; Zbl 1099.35134) Full Text: DOI Euclid
Merle, Frank Existence of blow-up solutions in the energy space for the critical generalized KdV equation. (English) Zbl 0970.35128 J. Am. Math. Soc. 14, No. 3, 555-578 (2001). Reviewer: Youssef Jabri (Oujda) MSC: 35Q53 35Q55 35B35 37K45 PDFBibTeX XMLCite \textit{F. Merle}, J. Am. Math. Soc. 14, No. 3, 555--578 (2001; Zbl 0970.35128) Full Text: DOI