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Organizing Committee
Stony Brook University
Brown University
Seoul National University
University of Southern California
Princeton University
Abstract
This workshop focuses on advancing the mathematical understanding of fluid dynamics, particularly the intricate phenomenon of turbulence. It aims to explore recent breakthroughs in the analysis of fluid equations, such as the Navier-Stokes and Euler equations, addressing fundamental questions of well-posedness, singularity formation, stability, and anomalous energy dissipation.
The workshop will explore cutting-edge mathematical techniques, including singularity formation, anomalous dissipation, convex integration, optimal transport, and regularity theory for partial differential equations.
The workshop will explore cutting-edge mathematical techniques, including singularity formation, anomalous dissipation, convex integration, optimal transport, and regularity theory for partial differential equations.
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Workshop Schedule
Saturday, November 22, 2025
8:50 - 9:00 AM EST
Welcome
11th Floor Lecture Hall
Brendan Hassett, ICERM/Brown University
9:00 - 9:45 AM EST
Non-uniqueness and vanishing viscosity in the forced 2D Euler equations
11th Floor Lecture Hall
Speaker
Dallas Albritton, University of Wisconsin-Madison
Session Chair
Theodore Drivas, Stony Brook University
Abstract
The forced 2D Euler equations exhibit non-unique solutions with vorticity in L^p, p > 1, whereas the corresponding Navier-Stokes solutions are unique. We investigate whether the inviscid limit from the forced 2D Navier-Stokes to Euler equations is a selection principle capable of "resolving" the non-uniqueness. We focus on solutions in a neighborhood of the non-uniqueness scenario discovered by Vishik; specifically, we incorporate viscosity and consider epsilon-size perturbations of his initial datum. We discover a uniqueness threshold below which the vanishing viscosity solution is unique and radial, and at which certain vanishing viscosity solutions converge to non-unique, non-radial solutions.
10:00 - 10:30 AM EST
Coffee Break
11th Floor Collaborative Space
10:30 - 11:15 AM EST
Navier-Stokes equations at critical regularity
11th Floor Lecture Hall
Speaker
Stan Palasek, Institute for Advanced Study
Session Chair
Theodore Drivas, Stony Brook University
Abstract
I will discuss questions related to well-posedness of the 3D Navier-Stokes equations at the critical regularity. In certain borderline spaces, global well-posedness is known only for small data, while the situation for mild solutions with large data is broadly open. We present some negative results in this setting including examples of non-uniqueness, arbitrary norm growth, and instantaneous blow-up.
11:30 AM - 12:15 PM EST
Singularity formation for incompressible fluids
11th Floor Lecture Hall
Speaker
Luis Martinez Zoroa, University of Basel
Session Chair
Wojciech Ożański, Princeton University
Abstract
In this talk we will discuss some of the recent developements in singularity formation for incompressible fluids, talking about various models, including IPM, Boussinesq and 3D Euler.
12:30 - 2:30 PM EST
Lunch/Free Time
2:30 - 3:15 PM EST
Classical Euler flows generate the strong Guderley imploding shockwave
Virtual
Virtual Speaker
Steve Shkoller, University of California, Davis
Session Chair
Javier Gomez Serrano, Brown University
Abstract
We prove that the classical Guderley imploding shock for the compressible Euler equations can be realized from smooth, radially symmetric initial data. The evolution is smooth up to the time of first singularity, when a preshock forms with a 1/3-cusp. From this preshock, a unique regular shock is born; it persists, strengthens, and ultimately focuses at the origin. On a time interval strictly prior to focusing, the solution agrees exactly with the self‑similar Guderley profile. As the focusing time is approached, the pressure and energy diverge while the density remains bounded. The analysis treats the shock as a moving interface coupled to the flow through the jump conditions and characteristic transport, and it quantifies how the solution locks onto the Guderley profile while the shock strength amplifies from weak to strong. Joint work with G. Cialdea and V. Vicol.
3:30 - 4:00 PM EST
Coffee Break
11th Floor Collaborative Space
4:00 - 4:45 PM EST
On stable implosions
11th Floor Lecture Hall
Speaker
Vlad Vicol, Courant Institute of Mathematical Sciences, New York University
Session Chair
Javier Gomez Serrano, Brown University
Abstract
We exhibit a new class of self-similar implosion solutions for the full compressible Euler equations. For any value of the adiabatic exponent, we construct a sequence of implosion profiles which are smooth (real analytic before collapse) and have an explicit similarity exponent (a closed-form expression). The first profile in this sequence (the ''ground state'') possesses remarkable stability properties, making it an ideal benchmark for multi-d Euler codes. This is joint work with J. Chen (U Chicago) and S. Shkoller (UC Davis).
5:00 - 6:30 PM EST
Reception
11th Floor Collaborative Space
Sunday, November 23, 2025
9:00 - 9:45 AM EST
Global well-posedness for the one-phase Muskat problem with or without surface tension
11th Floor Lecture Hall
Speaker
Hongjie Dong, Brown University
Session Chair
Wojciech Ożański, Princeton University
Abstract
We study the free boundary problem for 2D and 3D incompressible flow in porous media, known as the one-phase Muskat problem. In the absence of surface tension, we prove that when the initial interface is given by a Lipschitz graph, there exists a unique global Lipschitz strong solution. When surface tension is included, we establish small-data global well-posedness results in both the whole-space and periodic settings. This talk is based on joint work with Francisco Gancedo (Universidad de Sevilla), Huy Q. Nguyen (University of Maryland), and Hyunwoo (Will) Kwon (Brown University).
10:00 - 10:30 AM EST
Coffee Break
11th Floor Collaborative Space
Request Reimbursement
This section is for general purposes only and does not indicate that all attendees receive funding. Please refer to your personalized invitation to review your offer.
- ORCID iD
- As this program is funded by the National Science Foundation (NSF), ICERM is required to collect your ORCID iD if you are receiving funding to attend this program. Be sure to add your ORCID iD to your Cube profile as soon as possible to avoid delaying your reimbursement.
- Acceptable Costs
- 1 roundtrip between your home institute and ICERM
- Flights in economy class to either Providence airport (PVD) or Boston airport (BOS)
- Ground Transportation to and from airports and ICERM.
- Unacceptable Costs
- Flights on U.K. airlines
- Seats in economy plus, business class, or first class
- Change ticket fees of any kind
- Multi-use bus passes
- Meals or incidentals
- Advance Approval Required
- Personal car travel to ICERM from outside New England
- Multiple-destination plane ticket; does not include layovers to reach ICERM
- Arriving or departing from ICERM more than a day before or day after the program
- Multiple trips to ICERM
- Rental car to/from ICERM
- Arriving or departing from airport other than PVD/BOS or home institution’s local airport
- 2 one-way plane tickets to create a roundtrip (often purchased from Expedia, Orbitz, etc.)
- Travel Maximum Contributions
- New England: $350
- Other contiguous US: $850
- Asia & Oceania: $2,000
- All other locations: $1,500
- Note these rates were updated in Spring 2023 and supersede any prior invitation rates.
- Reimbursement Requests
Request Reimbursement with Cube
Refer to the back of your ID badge for more information. Checklists are available at the front desk and in the Reimbursement section of Cube.
- Reimbursement Tips
- Scanned original receipts are required for all expenses
- Airfare receipt must show full itinerary and payment
- ICERM does not offer per diem or meal reimbursement
- Allowable mileage is reimbursed at prevailing IRS Business Rate and trip documented via Google Maps PDF
- Keep all documentation until you receive your reimbursement!
- Reimbursement Timing
6–8 weeks after all documentation is sent to ICERM. All reimbursements are reviewed by multiple Brown University offices.
- Reimbursement Deadline
Submissions must be received within 30 days of ICERM departure to avoid applicable taxes. No submissions are accepted after six months.