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Date Time |
Location | Speaker |
Title – click for abstract |
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01/23 3:00pm |
BLOC 302 |
Yiran Hu University of Texas at Austin |
Global in time solutions to a family of 3D Quasi-Geostrophic Systems
Geophysicists have studied 3D Quasi-Geostrophic systems extensively. These systems describe stratified atmospheric flows on a large time scale and are widely used for forecasting atmospheric circulation. They couple an inviscid transport equation in $\mathbb{R}_{+}\times\Omega$ with an equation on the boundary satisfied by the trace, where $\Omega$ is either $2D$ torus or a bounded domain in $\rt$. In this talk, I will show the existence and some regularity results of global in time solutions to a family of singular 3D quasi-geostrophic systems with Ekman pumping, where the background density profile degenerates at the boundary. The main difficulty is handling the degeneration of the background density profile at the boundary. |
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02/27 3:00pm |
BLOC 302 |
Claude Bardos Laboratoire J.-L.Lions |
About large medium and shortime behavior of solutions of the collision of the Vlasov equation
TBA |
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02/27 4:00pm |
BLOC 302 |
Matthias Hieber Technische Universität Darmstadt |
Analysis of Nematic Liquid Crystal Flows: The Ericksen-Leslie and the Q-Tensor Model
In this talk we consider two models describing the flow of nematic liquid crystals: the Ericksen-Leslie model and the Q-tensor model. We discuss local as well as global well-posedness results for strong solutions in the incompressible and compressible setting and investigate as well equlibrium sets and the longtime behaviour of solutions. This is joint work with A. Hussein, J. Pruss and M. Wrona. |
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03/19 3:00pm |
BLOC 302 |
Marita Thomas Freie Universitaet - Berlin |
Analysis of a model for visco-elastoplastic two-phase flows in geodynamics
A model for an incompressible fluid of both viscoelastic and viscoplastic behavior is revisited, which is used in geodynamics, e.g., to describe the evolution of fault systems in the lithosphere on geological time scales. The Cauchy stress of this fluid is composed of a viscoelastic Stokes-like contribution and of an additional internal stress. The model thus couples the momentum balance with the evolution law of this extra stress, which features the Zaremba-Jaumann time-derivative and a non-smooth viscoplastic dissipation mechanism. This model is augmented to the situation of a bi-phasic material that undergoes phase separation according to a Cahn-Hilliard-type evolution law. Suitable concepts of weak solutions are discussed for the coupled
model. This is joint work with Fan Cheng (FU Berlin) and Robert Lasarzik (WIAS and FU Berlin) within project C09 'Dynamics of rock dehydration on multiple scales' of CRC 1114 'Scaling Cascades in Complex Systems' funded by the German Research Foundation.
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03/22 1:50pm |
BLOC 302 |
Daniel Boutros University of Cambridge |
On energy conservation for inviscid hydrodynamic equations: analogues of Onsager's conjecture
Onsager's conjecture states that 1/3 is the critical spatial (Hölder) regularity threshold for energy conservation by weak solutions of the incompressible Euler equations. We consider an analogue of Onsager's conjecture for the inviscid primitive equations of oceanic and atmospheric dynamics. The anisotropic nature of these equations allows us to introduce new types of weak solutions and prove a range of independent sufficient criteria for energy conservation. Therefore there probably is a 'family' of Onsager conjectures for these equations.
Furthermore, we employ the method of convex integration to show the nonuniqueness of weak solutions to the inviscid and viscous primitive equations (and also the Prandtl equations), and to construct examples of solutions that do not conserve energy in the inviscid case. Finally, we present a regularity result for the pressure in the Euler equations, which is of relevance to the Onsager conjecture in the presence of physical boundaries. As an essential part of the proof, we introduce a new weaker notion of pressure boundary condition which we show to be necessary by means of an explicit example. These results are joint works with Claude Bardos, Simon Markfelder and Edriss S. Titi. |
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03/26 3:00pm |
BLOC 302 |
Dehua Wang University of Pittsburgh |
Hyperbolic and mixed-type problems in gas dynamics and geometry
We shall consider the hyperbolic and mixed-type problems arising in gas dynamics and geometry. In particular, the transonic flows past obstacles and in nozzles as well as the isometric embedding in geometry will be discussed. |
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04/09 3:00pm |
BLOC 302 |
Yeyu Zhang Shanghai University of Finance and Economics |
Coupled Nonlinear Evolution and Inverse Energy Transfer in Moist Boussinesq Dynamics
The interaction between slow and fast components in geophysical fluid dynamics, especially under the influence of phase changes, poses significant analytical challenges. Our study develops a fast-wave averaging framework for the moist Boussinesq system, expanding past dry dynamics to include phase changes between water vapor and liquid water. We examine whether these phase transitions induce coupling between slow and fast waves or if the slow component evolves independently. Numerical simulations with a range of Froude and Rossby numbers reveal that phase changes may disrupt the proportionality of wave influence on the slow component, evidenced by a nonzero time-averaged wave component due to phase transitions. Furthermore, inverse energy transfer to larger scales is investigated in rotating and stratified flows, including water effects and rapid cloud microphysics. The findings could imply that potential vorticity, phase boundaries, and vertical velocity contribute to the formation of coherent structures in strongly rotated and stratified flows, appearing to indicate a revision to the traditional view of energy cascades in geophysical fluids. |
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04/09 4:00pm |
BLOC 302 |
Ricardo Alonso Texas A&M University - Qatar |
An energy method for the Boltzmann equation: Higher integrability and boundedness of solutions
We cover in detail an argument for proving higher integrability and uniform boundedness for solutions of the homogeneous Boltzmann equation. Techniques are reminiscent of the level set De Giorgi's method for classical elliptic/parabolic PDE. A rough idea of the method's implementation for the spatially inhomogenous problem is discussed at the end.
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04/16 03:00am |
BLOC 302 |
Angeliki Menegaki Imperial College London |
TBA
TBA |
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04/16 4:00pm |
BLOC 302 |
Aseel Farhat Florida State University |
TBA
TBA |
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04/30 3:00pm |
BLOC 302 |
Slim Ibrahim Univeristy of Victoria |
TBA
TBA |
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04/30 4:00pm |
BLOC 302 |
Quyuan Lin Clemson University |
TBA
TBA |