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- Arnaud Debussche

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
37
Citations
5,080
110
World Ranking
1701
National Ranking
100

- Mathematical analysis
- Partial differential equation
- Differential equation

Mathematical analysis, Stochastic partial differential equation, Uniqueness, Navier–Stokes equations and Multiplicative noise are his primary areas of study. His work on Mathematical analysis is being expanded to include thematically relevant topics such as Korteweg–de Vries equation. He combines subjects such as Initial value problem, Mathematical physics, Stochastic differential equation, Kinetic energy and Effective dimension with his study of Stochastic partial differential equation.

His biological study spans a wide range of topics, including Gibbs measure, Fixed point and Probability measure. His Hagen–Poiseuille flow from the Navier–Stokes equations study in the realm of Navier–Stokes equations interacts with subjects such as Martingale. His studies in Semigroup integrate themes in fields like Kolmogorov equations, Burgers' equation, Mixing and Ergodic theory.

- Strong solutions to the stochastic quantization equations (205 citations)
- Stochastic Burgers' equation (201 citations)
- Ergodicity for the 3D stochastic Navier–Stokes equations (164 citations)

His primary areas of investigation include Mathematical analysis, Stochastic partial differential equation, Partial differential equation, Mathematical physics and Applied mathematics. Multiplicative function is closely connected to Korteweg–de Vries equation in his research, which is encompassed under the umbrella topic of Mathematical analysis. His research in Stochastic partial differential equation tackles topics such as Stochastic differential equation which are related to areas like Diffusion equation.

His study explores the link between Partial differential equation and topics such as Statistical physics that cross with problems in Uniform norm. His work deals with themes such as Semigroup and Bounded function, which intersect with Mathematical physics. The Uniqueness study which covers Space that intersects with Mixing.

- Mathematical analysis (66.67%)
- Stochastic partial differential equation (30.23%)
- Partial differential equation (20.16%)

- Mathematical analysis (66.67%)
- Mathematical physics (18.60%)
- Stochastic partial differential equation (30.23%)

His primary areas of study are Mathematical analysis, Mathematical physics, Stochastic partial differential equation, Partial differential equation and Noise. His Mathematical analysis research focuses on subjects like Large deviations theory, which are linked to Periodic boundary conditions. His Mathematical physics study integrates concerns from other disciplines, such as Semigroup, Condensation and Gross–Pitaevskii equation.

Arnaud Debussche interconnects Wiener process and Applied mathematics in the investigation of issues within Stochastic partial differential equation. While the research belongs to areas of Wiener process, Arnaud Debussche spends his time largely on the problem of Initial value problem, intersecting his research to questions surrounding Kinetic energy. His Partial differential equation research includes elements of Weak solution, Uniform norm and Statistical physics.

- Degenerate parabolic stochastic partial differential equations: Quasilinear case (75 citations)
- A Regularity Result for Quasilinear Stochastic Partial Differential Equations of Parabolic Type (48 citations)
- Invariant measure of scalar first-order conservation laws with stochastic forcing (38 citations)

- Mathematical analysis
- Partial differential equation
- Differential equation

His scientific interests lie mostly in Stochastic partial differential equation, Mathematical analysis, Mathematical physics, Partial differential equation and Noise. The various areas that Arnaud Debussche examines in his Stochastic partial differential equation study include Itō's lemma, Initial value problem and Direct proof. His Hölder condition, Parabolic partial differential equation, Method of characteristics, Elliptic partial differential equation and Weak solution investigations are all subjects of Mathematical analysis research.

His Mathematical physics research incorporates themes from Space, Energy method and Schrödinger equation. His study connects Numerical analysis and Partial differential equation. In his papers, Arnaud Debussche integrates diverse fields, such as Noise, Large deviations theory, Noise correlation, Order of accuracy, Split-step method and Numerical stability.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Stochastic Burgers' equation

Guiseppe Da Prato;Arnaud Debussche;Roger Temam.

Nodea-nonlinear Differential Equations and Applications **(1994)**

305 Citations

Strong solutions to the stochastic quantization equations

Giuseppe Da Prato;Arnaud Debussche.

Annals of Probability **(2003)**

240 Citations

Scalar conservation laws with stochastic forcing

Arnaud Debussche;Julien Vovelle.

Journal of Functional Analysis **(2010)**

212 Citations

Ergodicity for the 3D stochastic Navier–Stokes equations

Giuseppe Da Prato;Arnaud Debussche.

Journal de Mathématiques Pures et Appliquées **(2003)**

196 Citations

The Stochastic Nonlinear Schrödinger Equation in H 1

A. de Bouard;A. Debussche.

Stochastic Analysis and Applications **(2003)**

193 Citations

Two-Dimensional Navier--Stokes Equations Driven by a Space--Time White Noise

Giuseppe Da Prato;Arnaud Debussche.

Journal of Functional Analysis **(2002)**

183 Citations

A Stochastic Nonlinear Schrödinger Equation with Multiplicative Noise

A. de Bouard;A. Debussche.

Communications in Mathematical Physics **(1999)**

174 Citations

On the Stochastic Korteweg–de Vries Equation

A de Bouard;A Debussche.

Journal of Functional Analysis **(1998)**

170 Citations

Weak approximation of stochastic partial differential equations: the nonlinear case

Arnaud Debussche.

Mathematics of Computation **(2010)**

162 Citations

Numerical simulation of the stochastic Korteweg-de Vries equation

Arnaud Debussche;Jacques Printems.

Physica D: Nonlinear Phenomena **(1999)**

158 Citations

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