## SIAG/Analysis of Partial Differential Equations Prize

The SIAM Activity Group on Analysis of Partial Differential Equations (SIAG/APDE) Prize, established in 2005, is awarded to the author(s) of the most outstanding paper, as determined by the prize committee, on a topic in partial differential equations. The contributions must be contained in a paper or papers published in English in a peer-reviewed journal.

The prize is awarded every two years at the **SIAM conference on
Analysis of Partial Differential Equations**. The
next award will be made in
**December 2019**.
The nomination period for the 2019 prize has closed.

## December 2017 Prize

**Scott N. Armstrong**(Courant Institute, USA) and

**Charles K. Smart**(University of Chicago, USA), were awarded the SIAG/APDE Prize at the SIAM Conference on Analysis of Partial Differential Equations held in Baltimore, Md, December 9-12, 2017.

They received the SIAG/APDE Prize for their paper "Quantitative stochastic homogenization of convex integral functionals", Annales Scientifiques de L'École Normale Supérieure, 49, 2016.

This work obtained outstanding results and developed fundamental new techniques which have greatly advanced the field and have opened the path to further developments.

Scott Armstrong delivered the prize lecture "Quantitative Stochastic Homogenization by Variational Methods" at a plenary session on December 11, 2017.

2017 SIAG/APDE Prize Award winners Scott Armstrong (left) and Charles Smart (right). |

More about their work can be found in their

**SIAM News inetrview**

The Prize Selection Commitee was chaired by Dejan Slepcev (Carnegie Mellon University) with members Lawrence Craig Evans (recused, UC Berkeley) Alessio Figalli (UT Austin and ETH Zurich) Anna Mazzucato (Pennsylvania State University) and Kevin Zumbrun (Indiana University Bloomington).

## December 2015 Prize

**Mathew A. Johnson**(University of Kansas, USA),

**Pascal Noble**(Institut de Mathèmatiques de Toulouse, France),

**Miguel Rodrigues**(Universitè de Rennes, France), and

**Kevin Zumbrun**(Indiana University, USA) were awarded the SIAG/APDE Prize at the SIAM Conference on Analysis of Partial Differential Equations held in Scottsdale, AZ, December 7-10, 2015.

They received the SIAG/APDE Prize for their paper " Behavior of Periodic Solutions of Viscous Conservation Laws Under Localized and Nonlocalized Perturbations ", Inventiones Mathematicae, Volume 197, Issue 1, 2014.

This paper gives a comprehensive rigorous answer to the stability and asymptotic behavior of periodic traveling wave solutions for a large class of dissipative systems including reaction-diffusion models and general systems of conservation or balance laws.

Miguel Rodrigues delivered the prize lecture at a plenary session on December 9, 2015.

2015 SIAG/APDE Prize Award Ceremony (Left to right: Helena Nussenzveig Lopes, Mathew Johnson, Miguel Rodrigues, and Kevin Zumbrun) |

The Prize Selection Commitee was chaired by Catherine Sulem, University of Toronto, with members Irene Gamba, University of Texas at Austin, Eitan Tadmor, University of Maryland, College Park, Athanasios Tzavaras, University of Crete, and Michael Weinstein, Columbia University.

## December 2013 Prize

**Camillo De Lellis**(Universität Zurich) and

**László Székelyhidi Jr.**(Universität Leipzig) were awarded the SIAG/APDE Prize at the SIAM Conference on Analysis of Partial Differential Equations held in Lake Buena Vista, Florida, December 7-10, 2013.

They received the SIAG/APDE Prize for their paper " The Euler Equation as a Differential Inclusion ", Annals of Mathematics, Volume 170, Number 3, 2009, 1417 - 1436.

The Prize Selection Committee found that this article is highly innovative and original, provides groundbreaking results on the Euler equation and in fact one of the best PDE results in recent years: "A highly innovative and influential paper which presents groundbreaking results on the Euler equation. One of the best results in PDEs in recent years."

The prize was received by László Székelyhidi who delivered the prize lecture at a plenary session on December 9, 2013. (Presentation.)

László Székelyhidi delivers the 2013 SIAG/ADPE Prize Lecture. |

The Prize Selection Commitee was chaired by Konstantina Trivisa, University of Maryland with members Luis Caffarelli, University of Texas at Austin, Nader Masmoudi, Courant Institute New York University, Helena Nussenzveig-Lopes, Universidade Federal do Rio de Janeiro, Sylvia Serfaty, UPMC Université Paris 6.

2013 SIAG/APDE Prize Award Ceremony (Left to right: Anna Mazzucato,Catherine Sulem, László Székelyhidi, Suncica Canic, and Edriss Titi ) |

## December 2011 Prize

**Gui-Qiang Chen**(Oxford University) and

**Mikhail Feldman**(University of Wisconsin-Madison) were awarded the SIAG/APDE Prize at the SIAM Conference on Analysis of Partial Differential Equations held in San Diego, California, December 14-17, 2011.

They received the SIAG/APDE Prize for their paper " Global solutions of shock reflection by large-angle wedges for potential flow," Annals of Mathematics, Volume 171, Number 2, 2010, 1067 - 1182.

The prize was received by Gui-Qiang Cheng who delivered the prize lecture at a plenary session on December 16, 2011 (Presentation.).

The Prize Selection Commitee was chaired by Stuart S. Antman (Acting Chair), University of Maryland, with members Helge Holden, NTNU-Norwegian University of Science and Technology, David Jerison, Massachusetts Institute of Technology, and Mary Pugh, University of Toronto

## December 2009 Prize

The paper "Global Well-Posedness of the Three-Dimensional Viscous Primitive Equations of Large Scale Ocean and Atmosphere Dynamics," Annals of Mathematics, Volume 166 (2007), written jointly by

**Edriss Titi**and his former student

**Chongsheng Cao**from University of California-Irvine has won the SIAM activity group in Analysis of PDEs Prize for the best paper in PDE in the last 4 years in recognition of its insight into the special structure of the pressure, based on velocity averages and fluctuations, and its impact on regularity and global existence of strong solutions.

The above paper provides a solution to a long-standing open problem with applications, that of global existence of strong solutions to the boundary-value problem for the 3-D viscous primitive equations, which have been used for many years as a model for weather, climate, and global ocean circulation. The authors solved this problem by developing important new insights that led to a proof of regularity of solutions.

The existence of weak solutions to this problem had been established in 1992 by J. L. Lions, Temam, and S. Wang, and short-time existence of strong solutions was proved in 2003 by Hu, Temam, and Ziane. The primitive equations are based on the Navier-Stokes equations, and as in that model, the difficulty in proving global regularity is to control the pressure. Cao and Titi's work developed a physically motivated decomposition of the velocity into mean and fluctuation and then exploited the resulting special structure of the pressure. They proved regularity by using this structure and ideas of Ladyzhenskaya, Prodi and Serrin from the 1960's that characterized strong solutions of the 3-D Navier-Stokes equations as those whose velocity field is in a certain regularity class.

The results of this paper surprised many experts in the field.

The award was presented at the SIAM Activity Group in Analysis of PDEs in Miami between December 7-10, 2009. Edriss gave the plenary talk about this work at the meeting.

SIAG/ADPE Prize Award Ceremony (L-R Chongsheng Cao,Gui-Qiang Chen, Edriss Titi) |

SIAG/APDE Prize Award Ceremony (L-R Patricia Bauman, Konstantina Trivisa, Gui-Qiang Chen, Chongsheng Cao, Edriss Titi, Irene Gamba) |

__Details__

The prize committee included Chair Patricia Bauman (Purdue University); Fang-Hua Lin (New York University); Ricardo Nochetto (University of Maryland); Michael Shearer (North Carolina State University); and Vladimir Sverak (University of Minnesota).

## December 2007 Prize

**Stefano Bianchini**(SISSA-ISAS, Italy) and

**Alberto Bressan**(Pennsylvania State University) were awarded the SIAG/APDE Prize at the SIAM (Society for Industrial and Applied Mathematics) Annual Meeting held in Mesa, Arizona, December 10-12, 2007.

They received the SIAG/APDE Prize for their paper "Vanishing Viscosity Solutions of Nonlinear Hyperbolic Systems," Annals of Mathematics, Volume 161, Number 1, 2005. (Ann. of Math. Volume 161, Number 1 (2005), 223-342.)

The prize was received by Stefano Bianchini who delivered the prize lecture at a plenary session on Tuesday, December 11, 2007.

Stefano Bianchini [SIAG-APDE 08, Mesa, Arizona] (December 11, 2007) |

SIAG/APDE Prize Award Ceremony (L-R Patty Bauman, Irene M. Gamba, Stefano Bianchini, Carme Calderer, Kevin Zumbrun) |

__Details__

The prize committee was chaired by Mary Pugh, with members Yann Brenier, Alice Chang, Bjorn Engquist, and Robert Pego.

See the SIAM website for details about the prize.

The next APDE prize will be awarded at the forthcoming 2009 APDE conference.

## July 2006 Prize

**Francois Golse**and

**Laure Saint-Raymond**were awarded the SIAG/APDE Prize at the SIAM (Society for Industrial and Applied Mathematics) Annual Meeting which was held in Boston,MA on July 10, 2006.

They received the SIAG/APDE Prize for their paper, "The Navier-Stokes Limit of the Boltzmann Equation for Bounded Collision Kernels," Inventiones Mathematicae, Volume 155, Number 1 2004, in recognition of making the definitive connection between weak solutions of the Boltzmann equation and Leray solutions of the incompressible Navier-Stokes equation.

Francois Golse accepted the award of a certificate and plaque at the Awards Luncheon of the SIAM Annual Meeting. He delivered a lecture based on the paper in a plenary session of the APDE conference.

__Biography (Golse)__

Francois Golse received his Ph.D. in Mathematics from the Universite Paris XIII in 1986, and joined the faculty. In 1987, he became a Centre National de la Recherche Scientifique (CNRS) research scientist at the Ecole Normale Superieure.

In 1993, he joined the faculty of the Universite Paris VI. In 2006, he was elected Professor of Mathematics at the Ecole Polytechnique in Paris.

Professor Golse is a member of the Institut Universitaire de France and has received several awards, including the Louis Armand Prize from the French Academy of Sciences and the Claude-Antoine Peccot Award from the College of France.

His research has focused on the study of problems in mathematical physics, including the Boltzmann equation, the time dependent Hartree-Fock approximation, the distribution of free path lengths in the Lorentz gas, and the fluid dynamic limits of kinetic equations.

__Biography (Saint-Raymond)__

Laure Saint-Raymond received her Ph.D. in Applied Mathematics from the Universite Paris VII in 2000. She joined the Centre National de la Recherche Scientifique (CNRS) as a research scientist in the Laboratoire d'Analyse Numerique, Universite Paris VI.

In 2002, she became a professor in the Laboratoire J.-L. Lions, Universite Paris VI. She has received several awards, including the Louis Armand Prize from the French Academy of Sciences, the Claude-Antoine Peccot Award from the College of France, and the Pius XI Gold Medal from the Pontificia Academia Scientarium.

Professor Saint-Raymond's research has focused on the study of charged particles submitted to strong constant external magnetic fields, for example, in tokamaks and plasmas in planetary environments. From a purely mathematical perspective, her interests are in the kinetic theory of rarefied flows and the problems of singular perturbations. This work allows a rigorous multiscale analysis of the motion of plasmas. These results can be easily transposed to problems of rotating fluids subject to the Coriolis force.

__Details__

See the SIAM website for details about the prize.

The prize committee was chaired by Walter Strauss, with members Patricia E Bauman, Craig Evans, Paul Fife, Philippe G. LeFloch.

The next APDE prize will be awarded at the December 10-12, 2007 APDE conference.

*Award announcement above is a modified version of the SIAM announcement.*

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