What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Quantum mechanics
- Geometry
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.
His most cited work include:
- On universality of blow-up profile for L 2 critical nonlinear Schrödinger equation (235 citations)
- On universality of blow-up profile for L 2 critical nonlinear Schrödinger equation (235 citations)
- The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation (229 citations)
What are the main themes of his work throughout his whole career to date?
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.
He most often published in these fields:
- Mathematical analysis (69.09%)
- Mathematical physics (47.27%)
- Nonlinear system (29.09%)
What were the highlights of his more recent work (between 2014-2021)?
- Mathematical analysis (69.09%)
- Mathematical physics (47.27%)
- Wave equation (21.82%)
In recent papers he was focusing on the following fields of study:
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.
Between 2014 and 2021, his most popular works were:
- Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schrödinger equations (33 citations)
- Type II blow up for the energy supercritical NLS (24 citations)
- On strongly anisotropic type I blow up (13 citations)
In his most recent research, the most cited papers focused on:
- Mathematical analysis
- Quantum mechanics
- Geometry
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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