Wednesday, May 28
9:20-10:10 AM Yaguang Wang, Shanghai Jiao Tong University
Wellposedness and Regularization-by-noise for the Stochastic Prandtl Equation
In this talk, we study the local and global existence of analytic/Gevrey solutions to the stochastic Prandtl equation in two and three dimensions, from which we observe the regularization effect of the noise. This is a joint work with Meng Zhao.
10:10-10:40 AM Morning Tea Break
10:40-11:30 AM Kelei Wang, Wuhan University
A Liouville Theorem for Supercritical Fujita Equation
In this talk, I’ll discuss a Liouville theorem for ancient solutions to supercritical Fujita equations, which says if the solution is close to the ODE solution at large scales, then it must be the ODE solution. Then I’ll discuss some application of this Liouville theorem to the analysis of first time singularity in this problem. This is based on a joint work with Juncheng Wei and Ke Wu.
11:30 AM-1:30 PM Lunch Break
1:30-2:20 PM Franck Sueur, University of Luxembourg
Recent Results on the Eulerian and Lagrangian Controllability of the Incompressible Navier-Stokes and MHD Systems
One classical controllability issue for deterministic PDEs is to determine whether there is a localized forcing which drives the solution of the system to a targeted state. In this talk, I will give an overview of some recent results regarding this issue in the case of the incompressible Navier-Stokes and of the MHD systems. Depending on whether one aims at modifying the Eulerian fields (u and B) or (some of) the fluid particles' location, this respectively corresponds to the notion of Eulerian and Lagrangian controllability. In both cases, nonlinear and nonlocal effects will show up in a decisive way.
2:20-2:50 PM Afternoon Tea Break
2:50-3:40 PM Can Zhang, Wuhan University
Controllability and Observability for Parabolic Equations
In this talk, I first recall some classical results on observability or controllability for the linear and semilinear parabolic equations. Then I will introduce our recent works on observability inequalities from measurable sets for linear parabolic equations, and with applications for the null controllability of semilinear parabolic equations.
3:50-4:40 PM Manuel Rissel, NYU Shanghai
Controllability of Incompressible Fluids Using Degenerate Controls
Controllability captures the ability of a system to transition between prescribed states under the influence of external actions (controls). Using degenerate controls means allowing only a few degrees of freedom to act on a system. As a rule of thumb, a more degenerate controllability problem requires a more involved analysis exploiting the underlying mechanisms of the model (e.g., diffusion, convection, nonlinearity, nonlocal effects, scaling laws, …). In the context of incompressible fluids, a well-known open question is due to A. A. Agrachev, asking whether the Navier—Stokes system is approximately controllable by means of a finite-dimensional and physically localized force. In my talk, I will introduce this and other degenerate controllability problems, and I will present recent progress on the approximate controllability of incompressible fluids driven by degenerate controls.
4:40-4:50 PM Closing Remarks