2020 - Member of Academia Europaea
His scientific interests lie mostly in Mathematical analysis, Korteweg–de Vries equation, Mathematical physics, Wave equation and Finite time. His research integrates issues of Universality and Nonlinear system in his study of Mathematical analysis. His work carried out in the field of Korteweg–de Vries equation brings together such families of science as Soliton, Rigidity and Partial differential equation.
He has researched Mathematical physics in several fields, including Vries equation and Conservation law. In his study, Scaling is inextricably linked to Nonlinear phenomena, which falls within the broad field of Vries equation. His Wave equation research incorporates themes from Quantum electrodynamics and Energy.
The scientist’s investigation covers issues in Mathematical analysis, Mathematical physics, Nonlinear system, Wave equation and Soliton. His study in the field of Nonlinear Schrödinger equation, Bounded function and Upper and lower bounds also crosses realms of Finite time. His research in Bounded function tackles topics such as Scaling which are related to areas like Rigidity.
His Mathematical physics research includes elements of Korteweg–de Vries equation, Singularity, Instability and Schrödinger equation. Within one scientific family, Frank Merle focuses on topics pertaining to Heat equation under Nonlinear system, and may sometimes address concerns connected to Sobolev space. His work in Wave equation addresses issues such as Stationary solution, which are connected to fields such as Homogeneous space.
His primary scientific interests are in Mathematical analysis, Mathematical physics, Wave equation, Heat equation and Soliton. His study in Mathematical analysis focuses on Euler equations in particular. His research investigates the connection with Mathematical physics and areas like Anisotropy which intersect with concerns in Symmetry and Combinatorics.
His Wave equation research is multidisciplinary, relying on both Surface, Scaling and Bounded function. His study in Scaling is interdisciplinary in nature, drawing from both Universality, Rigidity, Compact space and Schrödinger equation. His studies in Soliton integrate themes in fields like Space and Schrödinger's cat.
Frank Merle focuses on Mathematical physics, Singularity, Heat equation, Scaling and Bounded function. His Mathematical physics research is multidisciplinary, incorporating elements of Energy and Nonlinear system. His Singularity research is multidisciplinary, incorporating perspectives in Flow and Euler equations.
His Scaling study combines topics from a wide range of disciplines, such as Rigidity, Compact space, Wave equation and Schrödinger equation. To a larger extent, Frank Merle studies Mathematical analysis with the aim of understanding Compact space. In general Mathematical analysis study, his work on Spectral gap often relates to the realm of Implosion, thereby connecting several areas of interest.
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Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case
Carlos E. Kenig;Frank Merle.
Inventiones Mathematicae (2006)
Uniform estimates and blow–up behavior for solutions of −δ(u)=v(x)eu in two dimensions
Haïm Brezis;Frank Merle.
Communications in Partial Differential Equations (1991)
Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation
Carlos E. Kenig;Frank Merle.
Acta Mathematica (2008)
The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation
Frank Merle;Pierre Raphaël.
Annals of Mathematics (2005)
Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation
Frank Merle;Pierre Raphael.
Journal of the American Mathematical Society (2003)
On universality of blow-up profile for L 2 critical nonlinear Schrödinger equation
Frank Merle;Frank Merle;Pierre Raphael.
Inventiones Mathematicae (2004)
Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power
Duke Mathematical Journal (1993)
Construction of solutions with exactly $k$ blow-up points for the Schrödinger equation with critical nonlinearity
Communications in Mathematical Physics (1990)
Compactness at blow-up time for L2 solutions of the critical nonlinear Schrödinger equation in 2D
F. Merle;L. Vega.
International Mathematics Research Notices (1998)
L2 concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity
Frank Merle;Yoshio Tsutsumi.
Journal of Differential Equations (1990)
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