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UID:eec962f9736349ddba2cd6c856135245
CATEGORIES:Hyperbolic & Dispersive PDE Seminar
CREATED:20230906T122040
SUMMARY:Jared Speck - The structure of the maximal development for shock-forming 3D compressible Euler solution 
LOCATION: Hill 425
DESCRIPTION:Jared Speck Vanderbilt University\nSeptember 14, 2023, Thursday, 3:30-4:30p
 m, Hill 705\nTHE STRUCTURE OF THE MAXIMAL DEVELOPMENT FORSHOCK-FORMING 3D C
 OMPRESSIBLE EULER SOLUTION\nI will discuss my ongoing series of works with 
 L. Abbrescia on 3D compressible Euler flow. In these works, we derive the c
 omplete structure of a localized portion of the maximal development for ope
 nsets of initial data without symmetry, irrotationality, or isentropicity a
 ssumptions. In particular, we describe the full structure of a localized po
 rtion of the singular set, where the solution’s gradient blows up in a shoc
 k singularity, as well as the emergence of a localized piece of a Cauchy ho
 rizon from the singularity. Our work builds on Christodoulou’s breakthrough
  monographs on irrotational solutions and my prior works with J. Luk, which
  revealed an implicit portion of the singular set. The key new ingredients 
 are rough foliations of spacetime adapted to the shape of the boundary and 
 a geo-analytic framework that yields suitable estimates on the foliations. 
 Finally, I will discuss some of the many open problems in the field.\n
X-ALT-DESC;FMTTYPE=text/html:<p style="text-align: center;"><strong style="margin: 0px; padding: 0px; bo
 rder: none; outline: none; background-color: #ffffff; color: #111111; font-
 family: Palatino; font-size: 18px; letter-spacing: normal; orphans: 2; text
 -align: left; text-indent: 0px; text-transform: none; widows: 2; word-spaci
 ng: 0px; white-space: normal;">Jared Speck&nbsp;</strong>Vanderbilt Univers
 ity</p><p style="text-align: center;">September 14, 2023, Thursday, 3:30-4:
 30pm, Hill 705</p><p style="text-align: center;">THE STRUCTURE OF THE MAXIM
 AL DEVELOPMENT FORSHOCK-FORMING 3D COMPRESSIBLE EULER SOLUTION</p><p style=
 "text-align: center;">I will discuss my ongoing series of works with L. Abb
 rescia on 3D compressible Euler flow. In these works, we derive the complet
 e structure of a localized portion of the maximal development for opensets 
 of initial data without symmetry, irrotationality, or isentropicity assumpt
 ions. In particular, we describe the full structure of a localized portion 
 of the singular set, where the solution’s gradient blows up in a shock sing
 ularity, as well as the emergence of a localized piece of a Cauchy horizon 
 from the singularity. Our work builds on Christodoulou’s breakthrough monog
 raphs on irrotational solutions and my prior works with J. Luk, which revea
 led an implicit portion of the singular set. The key new ingredients are ro
 ugh foliations of spacetime adapted to the shape of the boundary and a geo-
 analytic framework that yields suitable estimates on the foliations. Finall
 y, I will discuss some of the many open problems in the field.</p>
CONTACT:Jared Speck, Vanderbilt University
DTSTAMP:20260828T094306
DTSTART;TZID=America/New_York:20230914T143000
DTEND;TZID=America/New_York:20230914T153000
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