| Date: | April 15, 2025 |
| Time: | 4:00pm |
| Location: | Blocker 117 |
| Speaker: | Igor Kukavica, University of Southern California |
| Title: | Analyticity and its applications in PDEs - Foias Lecture I |
| Abstract: | We will explore the analyticity and Gevrey regularity of solutions to partial differential equations, drawing significant inspiration from the seminal 1989 work of Foias and Temam on the Gevrey regularity of Navier-Stokes solutions. In addition to examining the analyticity properties of these solutions, we will review their applications to a range of topics in PDEs, including unique continuation, complexity of solutions, inviscid limit problems, and control. |
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| Date: | April 16, 2025 |
| Time: | 4:00pm |
| Location: | Blocker 117 |
| Speaker: | Igor Kukavica, University of Southern California |
| Title: | On the inviscid limit for the Navier-Stokes equations - Foias Lecture II |
| Abstract: | The convergence of solutions of the Navier-Stokes equations to those of the Euler equations as viscosity approaches zero is a significant topic in fluid dynamics. We will review the available results, applications, and open problems in the field. |
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| Date: | April 17, 2025 |
| Time: | 4:00pm |
| Location: | Blocker 117 |
| Speaker: | Igor Kukavica, University of Southern California |
| Title: | Free boundary problems - Foias Lecture III |
| Abstract: | We will address the local existence of solutions to the water wave problem, modeled by the incompressible Euler equations in a domain with an evolving boundary. Our focus will be on the local existence of solutions for initial velocities that are rotational and belong to low-regularity Sobolev spaces.
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