# Registered Data

## [00608] Limit behavior and asymptotic properties in fluid mechanics

**Session Date & Time**:- 00608 (1/3) : 3E (Aug.23, 17:40-19:20)
- 00608 (2/3) : 4C (Aug.24, 13:20-15:00)
- 00608 (3/3) : 4D (Aug.24, 15:30-17:10)

**Type**: Proposal of Minisymposium**Abstract**: The mathematical analysis of problems from fluid mechanics under the passage to certain limits can lead to new insights into the underlying physics and can help to improve numerical implementations. This minisymposium brings together scientists studying such kinds of asymptotic behaviors in different settings. The speakers present their research on homogenization problems and singular limits for fluid models, as well as on long-time and far-field behavior of fluid flows. Bringing together scientists working on these very different kinds of limit problems might create synergies between their approaches that usually differ significantly.**Organizer(s)**: Thomas Eiter, Florian Oschmann**Classification**:__35Q35__,__76M45__,__76M50__**Speakers Info**:- Christian Seis (University of Münster)
- Keiichi Watanabe (Waseda University)
- Tomoki Takahashi (Nagoya University)
- Ana Leonor Silvestre (Department of Mathematics and CEMAT, Instituto Superior Técnico, Universidade de Lisboa)
- Yong Lu (Nanjing University)
- Roberta Marziani (TU Dortmund)
- Ewelina Zatorska (Imperial College London)
- Florian Oschmann (Czech Academy of Sciences)
- Aneta Wróblewska-Kamińska (Polish Academy of Science)
- David Gérard-Varet (Université Paris Cité)
- Jou chun Kuo (Waseda University)
- Helena Nussenzveig Lopes (Federal University of Rio de Janeiro)

**Talks in Minisymposium**:**[01575] $\Gamma$-convergence of nearly incompressible fluids****Author(s)**:- Peter Bella (TU Dortmund)
- Eduard Feireisl (Czech Academy of Sciences)
**Florian Oschmann**(Czech Academy of Sciences)

**Abstract**: We consider the time-dependent compressible Navier–Stokes equations in the low Mach number regime in a family of domains $\Omega_\varepsilon \subset \mathbb{R}^d$ converging in the sense of Mosco to a domain $\Omega \subset \mathbb{R}^d, \ d \in \{2,3\}$. We show the limit is the incompressible Navier–Stokes system in $\Omega$. This is joint work with Peter Bella $($TU Dortmund$)$ and Eduard Feireisl $($CAS$)$.

**[01603] Stokes and Oseen fundamental solutions: asymptotic properties of fluid flows and applications in computational fluid dynamics****Author(s)**:**Ana Leonor Silvestre**(Instituto Superior Técnico, Universidade de Lisboa)

**Abstract**: Starting from the Stokes and Oseen steady and unsteady fundamental solutions, we discuss asymptotic properties of fluid flow around a translating and rotating rigid body. This part of the talk includes joint work with Toshiaki Hishida, from Nagoya University, Japan, and Takéo Takahashi, from INRIA Nancy - Grand Est, France. In the second part of the talk, based on joint work with Carlos Alves, Rodrigo Serrão, from Instituto Superior Técnico, Portugal, and Svilen Valtchev, from Instituto Politécnico de Leiria, Portugal, we present a numerical study of the Method of Fundamental Solutions for Stokes and Oseen boundary value problems. The accuracy of the method is illustrated through a series of numerical tests, which include a comparison between analytic and numerical solutions and the application of the method to classical benchmark problems.

**[01787] Homogenization of nonstationary incompressible viscous non-Newtonian flows****Author(s)**:**Yong Lu**(NANJING UNIVERSITY)- Zhengmao Qian (NANJING UNIVERSITY)

**Abstract**: We consider the homogenization of the nonstationary incompressible viscous non-Newtonian fluid flows in a domain perforated with a large number of tiny holes, where the size of the holes is proportional to the mutual distance of the holes, and the stress tensor satisfies the Carreau-Yasuda law. Darcy's law is derived in the limit as the size of holes goes to zero and the number of holes goes to infinity simultaneously.

**[03881] The Navier-Stokes flow in the exterior Lipschitz domain****Author(s)**:**Keiichi Watanabe**(Suwa University of Science)

**Abstract**: Consider the three-dimensional Navier-Stokes equations in an exterior Lipschitz domain $\Omega$. In this talk, we show the unique existence of a global strong solution $u$ to the Navier-Stokes equations and investigate the large time behavior of the solution $u$. Although the boundary is not smooth, we show that the large time behavior of the Navier-Stokes flow is completely recovered in the exterior Lipschitz domain $\Omega$ along exactly the same argument as usual.

**[04114] Mixing and enhanced dissipation for fluid suspensions****Author(s)**:**David Gerard-Varet**(Universite Paris Cite et IMJ-PRG)

**Abstract**: We consider a model introduced by D. Saintillan and M. Shelley to describe active suspensions of elongated particles. This model couples a Stokes equation for the fluid substrate and a transport equation for the density distribution of particles in space and orientation. We investigate mixing properties of this model (damping and enhanced dissipation). The main new feature of the analysis is that the usual velocity variable of the euclidean space is replaced by an orientation variable on the sphere, which is responsible for strong qualitative changes and new mathematical difficulties. This is joint work with M. Coti Zelati and H. Dietert.

**[04533] Anisotropically spatial-temporal behavior of the Navier-Stokes flow past an obstacle****Author(s)**:**Tomoki Takahashi**(Tokyo Institute of Technology)

**Abstract**: We consider the spatial-temporal behavior of the Navier-Stokes flow past a three dimensional rigid body and deduce the temporal decay rate with the spatial weight caused by translation. The key tool is the $L^q$-$L^r$ estimate of the Oseen semigroup in exterior domains and we develop the weighted $L^q$ theory of the Oseen semigroup. New results on the Stokes semigroup in isotropic $L^q$ spaces are also discussed.

**[04660] Multiscale analysis - from compressible to incompressible system****Author(s)**:**Aneta Wróblewska-Kamińska**(Institute of Mathematics, Polish Academy of Sciences)

**Abstract**: We will show asymptotic analysis for hydrodynamic systems as a tool in in the situation when certain parameters vanish or become infinite. We will concentrate on rigorous mathematical analysis of low Mach number limits with so called ill-prepared dat. I will present some results which concerns passage from compressible to incompressible models including Navier-Stokes-Fourier system on varying domains, a multi-scale problem for viscous heat-conducting fluids in fast rotation and FENE model for dilute polymeric fluids.

**[04842] Invariant manifolds for the thin film equation****Author(s)**:**Christian Seis**(University of Munster)- Dominik Winkler (University of Munster)

**Abstract**: The large-time behavior of solutions to the thin film equation with linear mobility in the complete wetting regime on R^N is examined: We investigate the higher order asymptotics of solutions converging towards self-similar Smyth--Hill solutions under certain symmetry assumptions on the initial data. The analysis is based on a construction of finite-dimensional invariant manifolds that solutions approximate to an arbitrarily prescribed order.

**[05036] Resolvent estimate for the Stokes equations in the Besov spaces****Author(s)**:**Jou chun Kuo**(Graduate School of Fundamental Science and Engineering, Waseda University)

**Abstract**: This talk is devoted to proving the resolvent estimates of the linearized system of the compressible Navier-Stokes equations with homogeneous boundary conditions in the half-space. We construct the solution in $B^s_{q,1}$ for $1

**[05215] Conditions for energy balance in 2D incompressible ideal fluid flow****Author(s)**:- Milton da Costa Lopes Filho (Universidade Federal do Rio de Janeiro)
- Samuel Lanthaler (California Institute of Technology)
- Fabian Jin (ETH-Zurich)
**Helena Judith Nussenzveig Lopes**(Universidade Federal do Rio de Janeiro)

**Abstract**: In this talk I will discuss necessary and sufficient conditions on the regularity of the external force for energy balance to hold for weak solutions of the 2D incompressible Euler equations. This is motivated by turbulence modeling and the result is in contrast with the situation in 3D and the existence of wild solutions.

**[05422] Existence of weak solutions and hard-congestion limit in the dissipative Aw-Rascle system****Author(s)**:**Ewelina Zatorska**(Imperial College London)- Nilasis Chaudhuri (Imperial College London)

**Abstract**: In this talk I am going to present the dissipative Aw-Rascle model of evolution of congestions. I will first explain its connection with other models in fluid mechanics (compressible Euler and Navier-Stokes) and present our progress on the existence theory. In the second part of my talk I will focus on discussing a singular limit passage leading to the so-called "hard-congestion" system.