Frank Merle

Professor at Mathematics, University of Chicago0 Followers

Frank Merle transforms traditional models of mathematical thought through his role as a Visiting Professor in the Department of Mathematics at the University of Chicago. With a profound understanding of mathematical theories, he engages students and colleagues alike, fostering an environment of intellectual curiosity and exploration. His contributions to the academic community are marked by a commitment to advancing mathematical knowledge, though his specific research interests remain a mystery. At the University of Chicago, Frank Merle continues to inspire the next generation of mathematicians, encouraging them to push the boundaries of what is known and explore the vast possibilities within the field.

Research Interests

Mathematical theories intellectual curiosity mathematical exploration advancing mathematical knowledge

Publications

1 - On a sharp lower bound on the blow-up rate for the 𝐿² critical nonlinear Schrödinger equation,Journal of the American Mathematical Society

Frank Merle , Pierre Raphael ,

, 37-90, 2005-09-01

2 - On blow up for the energy super critical defocusing nonlinear Schrödinger equations,Inventiones mathematicae

Frank Merle , Pierre Raphaël , Igor Rodnianski , Jeremie Szeftel ,

, 247-413, 2021-09-15

3 - Multi solitary waves for nonlinear Schrödinger equations,Annales de l'Institut Henri Poincaré C, Analyse non linéaire

Yvan Martel , Frank Merle ,

, 849-864, 2006-12-01

4 - Strongly anisotropic type II blow up at an isolated point,Journal of the American Mathematical Society

Charles Collot , Frank Merle , Pierre Raphaël ,

, 527-607, 2020-02-20

5 - On Nonexistence of type II blowup for a supercritical nonlinear heat equation,Communications on Pure and Applied Mathematics

Hiroshi Matano , Frank Merle ,

, 1494-1541, 2004-08-26

6 - Asymptotics for L2 minimal blow-up solutions of critical nonlinear Schrödinger equation,Annales de l'Institut Henri Poincaré C, Analyse non linéaire

, 553-565, 1996-10-01

7 - Construction of multi-soliton solutions for the $L^2$-supercritical gKdV and NLS equations,Revista Matemática Iberoamericana

Raphaël Côte , Yvan Martel , Frank Merle ,

, 273-302, 2011-04-30

8 - Dynamics near explicit stationary solutions in similarity variables for solutions of a semilinear wave equation in higher dimensions,Transactions of the American Mathematical Society

Frank Merle , Hatem Zaag ,

, 27-87, 2015-04-15

9 - Blowup Solutions to the Semilinear Wave Equation with a Stylized Pyramid as a Blowup Surface,Communications on Pure and Applied Mathematics

Frank Merle , Hatem Zaag ,

, 1850-1937, 2018-05-17

10 - The instability of Bourgain-Wang solutions for the L 2 critical NLS,American Journal of Mathematics

Frank Merle , Pierre Raphaël , Jeremie Szeftel ,

, 967-1017, 2013-08-01

11 - Universality of blow-up profile for small radial type II blow-up solutions of the energy-critical wave equation,Journal of the European Mathematical Society

Thomas Duyckaerts , Carlos E. Kenig , Frank Merle ,

, 533-599, 2011-02-22

12 - THE EFFECT OF LEVEL AND FREQUENCY OF FEEDING WHOLE MILK ON BODY WEIGHT GAIN AND FEED CONVERSION OF CALVES,Canadian Journal of Animal Science

L. J. FISHER , FRANK VAN MERLE ,

, 473-476, 1983-06-01

13 - Blow up in finite time and dynamics of blow up solutions for the 𝐿²–critical generalized KdV equation,Journal of the American Mathematical Society

Yvan Martel , Frank Merle ,

, 617-664, 2002-03-08

14 - Behavior Rigidity Near Non-Isolated Blow-up Points for the Semilinear Heat Equation,International Mathematics Research Notices

Frank Merle , Hatem Zaag ,

, 16196-16260, 2021-07-16

15 - Solution of a nonlinear heat equation with arbitrarily given blow‐up points,Communications on Pure and Applied Mathematics

, 263-300, 1992-03-01

16 - On uniqueness and continuation properties after blow‐up time of self‐similar solutions of nonlinear schrödinger equation with critical exponent and critical mass,Communications on Pure and Applied Mathematics

, 203-254, 1992-02-01

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