# IV Workshop on Fluids and PDE

IMPA, Rio de Janeiro May 26 – 30, 2014

The main theme of the workshop is mathematical modeling and rigorous analysis of fluid dynamics problems, particularly incompressible flows with little regularity (non-smooth) and turbulent flows. It is a strategic area that touches on several relevant problems in applications such as aerodynamic flow modeling, turbulence modeling and analysis, turbulence flow, oceanographic and geophysical flows relevant to meteorology, etc. The scientific rationale in this area is subordinated to mathematical advances and is relatively undeveloped in Brazil; so this meeting was quite timely.

The research area dealing with these problems has generated intense activity over the last two decades. There is a research group in this area in Brazil, with concentration in Rio de Janeiro, but still needs to be consolidated. Expanding this state and national group is one of the main motivations of this event.

This workshop is held every two or three years in Brazil. Its fourth was the closing event of a thematic program on Dynamics of Incompressible Fluids, which was held at IMPA in the period from March 12 to June 12, 2014.

__Scientific Committee:__

Claude Bardos, University of Paris 7 – Denis Diderot (emeritus); Laboratory Jacques Louis Lions University of Paris 6—Pierre and Marie Curie; the Wolfgang Pauli Institute in Vienna.

John Gibbon, Imperial College London, England (emeritus)

Michael Jolly, Indiana University, Bloomington, IN, USA.

James Kelliher, University of California Riverside, USA.

Milton Lopes Filho, Universidade Federal do Rio de Janeiro, Brazil.

Helena Nussenzveig Lopes, Universidade Federal do Rio de Janeiro, Brazil.

Ricardo Rosa, Universidade Federal do Rio de Janeiro, Brazil.

Edriss Titi, University of California, Irvine; the Weizmann Institute in Rehovot, Israel.

__Organizing Committee:__

** **Milton da Costa Lopes Filho (UFRJ)

Ricardo Martins da Silva Rosa (UFRJ)

Helena Judith Nussenzveig Lopes (UFRJ)

**Plenary Talks:**

Long time behavior of the Navier-Stokes and related equations

**Alexey Cheskidov** (UIC)

Blowup as a driving mechanism of turbulence in shell mode

**Alexei Mailybaev** (IMPA)

Statistical Solutions from an Abstract Viewpoint,

**Cecília Mondaini** (UFRJ)

Wall to wall optimal transport

**Charlie Doering** (Univ. Michigan)

2D ideal flow through a porous medium

**Christophe Lacave** (Paris VII)

Viscosity Solutions and Wild Solutions

**Claude Bardos** – Université Paris VI

Continuous Data Assimilation for the three-dimensional Navier-Stokes model

**Débora Albanez** (UTFPR)

On the regularity of solutions for the Muskat problem

**Diego Cordoba** (CSIC)

An Algorithm for Advancing Slow Features in Fast-Slow Systems without Scale Separation – A Young Measure Approach

**Edriss Titi** (Weizmann Institute of Science and University of California – Irvine)

Renormalization Defects for Continuity Equations

**Emil Wiedemann** (UBC)

Finite-time blowup for a complex Ginzburg-Landau equation

**Flávio Dickstein** (UFRJ)

Non-homogeneous Navier-Stokes system with Navier friction boundary conditions

**Gabriela Planas** – IMECC (UNICAMP)

Boundary correctors and energy estimates for the boundary layer problem

**Helena J. Nussenzveig Lopes** (UFRJ)

On the size of the nodal sets of solutions of elliptic and parabolic PDEs

**Igor Kukavica** (USC)

Vortex patches redux

**James P Kelliher** (UCR)

Navier-Stokes equations with incompatible data in the zero viscosity limit

**Marco Sammartino** (PALERMO)

Decay characterization of solutions to dissipative systems

**Maria Schonbek** (UCSC)

On whether zero is in the global attractor of the 2D Navier-Stokes equations

**Michael Jolly** (IU)

Global strong solutions to the 3D primitive equations with only horizontal viscosities and diffusivity

**Jinkai Li** (WIS)

Invariant Measures and Inviscid Limits for the Stochastic Navier-Stokes Equations and Related Systems

**Nathan Glatt-Holtz** (Virginia Tech)

A prediction scheme for systems of partial differential equations with fast-determining variables

**Paul Krause** (UFSC)

Analyticity of Lagrangian Trajectories

**Peter Constantin** (PU)

Recurrence and convergence of time averages for the three-dimensional incompressible Navier-Stokes equations

**Ricardo M. S. Rosa** (UFRJ)

Shortwave instability of Rayleigh-Taylor dynamics

**Roman Shvydkoy** (UIC)

On some large time behaviors of the full water wave problem

**Sijue Wu** (UM)

Recent progress towards resolving Onsager’s Conjecture

**Tristan Buckmaster** (UNI)

Smallest scale estimates for the Navier-Stokes equations

**Vincent Martinez** (IU)

On the inviscid limit of the Navier-Stokes equations

**Vlad C Vicol** (PU)

Stochastic Hyperbolic Partial Differential Equations

**Wladimir Neves** (UFRJ)

Phase Field models for two phase flows in karstic geometry

**Xiaoming Wang** (FSU)

Global Well-posedness of a coupled KdV system of Majda and Biello

**Yanqiu Guo** (WIS)

**Short Talks:**

Convergence of the 2D Euler-α to Euler equations in the Dirichlet case: indifference to boundary layers

Aibin Zang (UFRJ)

On the self-similar blow-up scenario for the Euler equations

Anne Caroline Bronzi (UNB)

A new continuous data assimilation algorithm for the Bénard problem

Aseel Farhat (IU)

Statistical Solutions from an Abstract Viewpoint

Cecilia Freire Mondaini (UFRJ)

Continuous Data Assimilation for the three-dimensional Navier-Stokes-alpha model

Débora A. Francisco Albanez – IMECC (UNICAMP)

Global well-posednenss of strong solutions to the primitive equations

Jinkai Li (WIS)

On the Boundary Regularity for the 6D Stationary Navier-Stokes Equations

Jitao Liu (UFRRJ)

Existence and decay of solutions of the 2D QG equations in the presence of an obstacle

Leonardo Kosloff (UCR)

The Harnack inequality for elliptic and parabolic equations with divergence-free drifts of low regularity

Mihaela Ignatova (STANFORD)

The existence of a global attractor for the forced critical surface quasi-geostrophic Equation in L2

Mimi Dai (UIC)

Recent progress towards resolving Onsager’s Conjecture

Tristan Buckmaster (UNI)

Smallest scale estimates for the Navier-Stokes equations

Vincent R. Martinez (IU)

Global Well-posedness of a coupled KdV system of Majda and Biello

Yanqiu Guo (WIS)

**Posters:**

Applications of Euler equation in cosmology

Alan Toribio (UFES)

Grupos Discretos de Plano Hiperbólico

Carlos Anatoio Guimarães Silva (UFPB)

Asymptotic solutions near blowup in inviscid MHD shell model

Guilherme Tegoni Goedert (IMPA)

On the asymptotic behavior of solutions of the incompressible stationary Navier-Stokes equations in dimension three

Hugo Decaster (UCBL)

Characterization of Serfati vorticities

Maicon Benvenutti – IMECC (UNICAMP)

Implementation of finite elements mortar using lagrange multiplier in homogêneous coordinates – application to structures of microwaves

Moacir Moura de Andrade Filho (UNB)

Div-curl type estimates for elliptic systems ofc omplex vector elds

Tiago H. Picon (USP – FFCLRP)

**Postal Address: **Instituto Nacional de Matemática Pura e Aplicada

Estrada Dona Castorina 110, Jardim Botânico

Rio de Janeiro, RJ, CEP 22460-320, Brasil

E-mail: eventos@impa.br