CMC Intensive Lectures Date: October 12 & 14, 2016 Place: Rm. 8309, KIAS |
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Lecture series by Jörg Wolf (Humboldt-Universität zu Berlin)
Title: On partial regularity results for the 3D incompressible Navier-Stokes equations
Abstract: While the existence of a global weak solution to the Navier-Stokes equations has been known for a long time, the existence of a global classical solution for given smooth decaying initial data is still open and is one of the seven famous millennium problems of the Clay Institute (see http://www.claymath.org/millennium-problems). In our our series of lectures we shall present various regularity results for weak solutions to the Navier-Stokes equations. Our main objective will be to give a detailed proof of the celebrated Caffarelli-Kohn-Nirenberg theorem on the partial regularity of suitable weak solutions to the Navier-Stokes equations and a modern version of this theorem in general domains. The proof of the latter result is based on local energy estimate involving the velocity field only but not depending on the global pressure. Such estimates has been obtained recently by using the method of a local pressure projection.
Organizer & Contact:
Sung-Jin Oh (KIAS) / sjoh@kias.re.kr
Title: On partial regularity results for the 3D incompressible Navier-Stokes equations
Abstract: While the existence of a global weak solution to the Navier-Stokes equations has been known for a long time, the existence of a global classical solution for given smooth decaying initial data is still open and is one of the seven famous millennium problems of the Clay Institute (see http://www.claymath.org/millennium-problems). In our our series of lectures we shall present various regularity results for weak solutions to the Navier-Stokes equations. Our main objective will be to give a detailed proof of the celebrated Caffarelli-Kohn-Nirenberg theorem on the partial regularity of suitable weak solutions to the Navier-Stokes equations and a modern version of this theorem in general domains. The proof of the latter result is based on local energy estimate involving the velocity field only but not depending on the global pressure. Such estimates has been obtained recently by using the method of a local pressure projection.
| Time | Oct. 12 (Wed) | Oct. 14 (Fri) |
| 10:00 - 10:50 | Lecture 1 | Lecture 5 |
| 11:00 - 11:50 | Lecture 2 | Lecture 6 |
| Lunch | ||
| 14:00 - 15:20 | Lecture 3 | Lecture 7 |
| 16:00 - 17:30 | Lecture 4 | Lecture 8 |
Organizer & Contact:
Sung-Jin Oh (KIAS) / sjoh@kias.re.kr