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PRODID:Mathematics Seminar Calendar
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UID:20191121T215634-17489@math.msu.edu
DTSTAMP:20191121T215634Z
SUMMARY:Rough solutions to the three-dimensional compressible Euler equations with vorticity and entropy
DESCRIPTION:Speaker\: Marcelo Disconzi, Vanderbilt University\r\nWe prove a series of intimately related results tied to the regularity and geometry of solutions to the three-dimensional compressible Euler equations.\r\n\r\nThe solutions are allowed to have nontrivial vorticity and entropy, and an arbitrary equation of state with positive sound speed. The central theme is that under low regularity assumptions on the initial data, it is possible to avoid, at least for short times, the formation of shocks. Our main result is that the time of classical existence can be controlled under low regularity assumptions on the part of the initial data associated with propagation of sound waves in the fluid. Such low regularity assumptions are in fact optimal. To implement our approach, we derive several results of independent interest: (i) sharp estimates for the acoustic geometry, which in particular capture how the vorticity and entropy interact with the sound waves; (ii) Strichartz estimates for quasilinear sound waves coupled to vorticity and entropy; (iii) Schauder estimates for the transport-div-curl-part of the systems. Compared to previous works on low regularity, the main new feature of our result is that the quasilinear PDE system under study exhibit multiple speeds of propagation. In fact, this is the first result of its kind for a system with multiple characteristic speeds. An interesting feature of our proof is the use of techniques that originated in the study of the vacuum Einstein equations in general relativity.
LOCATION:C304 Wells Hall
DTSTART:20190911T201000Z
DTEND:20190911T210000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=17489
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UID:20191121T215634-19649@math.msu.edu
DTSTAMP:20191121T215634Z
SUMMARY:Unexpected combinatorial properties of all planar measures
DESCRIPTION:Speaker\: A. Volberg/P. Mozolyako\r\nWe will start with paraproducts--operators used in PDE to prove Leibniz rule with fractional derivatives. Then we move to bi-parameter paraproducts and prove the property from the title.
LOCATION:C517 Wells Hall
DTSTART:20190926T170000Z
DTEND:20190926T175000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=19649
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UID:20191121T215634-19670@math.msu.edu
DTSTAMP:20191121T215634Z
SUMMARY:Embedding on bi-tree
DESCRIPTION:Speaker\: Pavel Mozolyako, MSU\r\n
LOCATION:C517 Wells Hall
DTSTART:20191010T170000Z
DTEND:20191010T175000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=19670
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UID:20191121T215634-20694@math.msu.edu
DTSTAMP:20191121T215634Z
SUMMARY:A unified approach to three themes in harmonic analysis
DESCRIPTION:Speaker\: Victor Lie, Purdue University\r\n
LOCATION:C304 Wells Hall
DTSTART:20191101T170000Z
DTEND:20191101T180000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=20694
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UID:20191121T215634-19645@math.msu.edu
DTSTAMP:20191121T215634Z
SUMMARY:Derivation of a ternary Boltzmann system
DESCRIPTION:Speaker\: Ioakeim Ampatzoglou, University of Texas, Austin\r\nIn this talk work we present a rigorous derivation of a new kinetic equation describing the limiting behavior of a classical system of particles with three particle instantaneous interactions, which are modeled using\r\na non-symmetric version of a ternary distance. The equation, which we call ternary Boltzmann equation, can be understood as a step towards modeling a dense gas in non-equilibrium. This is a joint work with Natasa PavloviÄ‡.
LOCATION:C304 Wells Hall
DTSTART:20191106T211000Z
DTEND:20191106T220000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=19645
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UID:20191121T215634-20703@math.msu.edu
DTSTAMP:20191121T215634Z
SUMMARY:Regularity results for a class of Kolmogorov-Fokker-Planck equations in non-divergence form
DESCRIPTION:Speaker\: Farhan Abedin, Michigan State University\r\nThe Kolmogorov-Fokker-Planck equation is a degenerate parabolic equation arising in models of gas dynamics from kinetic theory. The operator is of the form\r\n$$\mathcal{L}_Au := \mathrm{tr}(A(v,y,t) D^2_v u) + v \cdot \nabla_yu - \partial_tu,$$ where $$u(v,y,t): \mathbb{R}^{2d+1} \to \mathbb{R} \text{ and } 0 < \lambda \mathbb{I}_d \leq A \leq \Lambda \mathbb{I}_d.$$\r\nIt is an open problem if non-negative solutions of $\mathcal{L}_A u = 0$ in $\mathbb{R}^{2d+1}$ satisfy a scale-invariant Harnack inequality, assuming the matrix coefficient $A$ is merely bounded and measurable. I will discuss recent joint work with Giulio Tralli in which progress is made on partially solving this problem.
LOCATION:C304 Wells Hall
DTSTART:20191113T211000Z
DTEND:20191113T220000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=20703
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BEGIN:VEVENT
UID:20191121T215634-20714@math.msu.edu
DTSTAMP:20191121T215634Z
SUMMARY:Stability of traveling planewave solutions to Lorentzian vanishing mean curvature flow
DESCRIPTION:Speaker\: Leonardo Abbrescia, MSU\r\nLorentzian minimal submanifolds of Minkowski space are the dynamic analogue of minimal surfaces in the elliptic regime. They are defined by the vanishing of mean curvature, which can be expressed as a system of geometric PDEs. With the requirement that the submanifold be Lorentzian, that is, that the induced metric is Lorentzian, the equations have a hyperbolic nature. Consequently, the natural approach to study them is via the Cauchy initial value problem. In this talk we discuss stability properties of traveling planewave solutions to these equations, and highlight the difficulties introduced by the "infinite energy" planewave background. This is joint work with Willie Wong.
LOCATION:C517 Wells Hall
DTSTART:20191121T180000Z
DTEND:20191121T185000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=20714
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