BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Marco Bravin DTSTART:20210617T073000Z DTEND:20210617T081500Z DTSTAMP:20260417T111237Z UID:Oneworldmeeting/1 DESCRIPTION:Title: The vortex filament equation and the well-posedness of the cubic N LS for irregular data\nby Marco Bravin as part of One world meeting of young mathematicians in fluid dynamics\n\n\nAbstract\nThe vortex filament equation (VFE) is a geometric equation that describes the evolution of a curve of vorticity in a three dimensional incompressible inviscid fluid. T hrough the Hasimoto transformation\, the VFE is associated with the cubic NLS equation. In this talk I will focus my attention on vortex filaments t hat are initially polygonal lines\, which correspond to studying the cubic NLS with sum of delta of Dirac as initial data. In particular I will show local and large in time well-posedness for sufficiently small initial dat a in appropriated spaces. This is a joint work with Luis Vega.\n LOCATION:https://researchseminars.org/talk/Oneworldmeeting/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Eduardo García-Juárez DTSTART:20210617T081500Z DTEND:20210617T090000Z DTSTAMP:20260417T111237Z UID:Oneworldmeeting/2 DESCRIPTION:Title: The Muskat and Peskin Problems with Viscosity Contrast\nby Edu ardo García-Juárez as part of One world meeting of young mathematicians in fluid dynamics\n\n\nAbstract\nThe Muskat problem studies the dynamics o f the interface between fluids in a porous medium governed by Darcy’s la w. The Peskin problem models the movement of a closed elastic filament imm ersed in an incompressible fluid. While the former is at the core of petro chemical engineering processes\, the latter is a prototypical test problem for biophysical fluid-structure modeling. On the mathematical side\, both systems are nonlinear and nonlocal PDEs\, of parabolic type\, and share t he same scaling. We will show how the use of some spaces based on the Wien er algebra turns out to be very convenient to analyze this kind of problem s\, yielding instant analytic smoothing\, global existence\, and convergen ce to the steady states. The techniques allow to consider non too-small in itial data\, critical regularity in terms of the natural scaling and diffe rent viscosities for each fluid.\n LOCATION:https://researchseminars.org/talk/Oneworldmeeting/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriela López Ruiz DTSTART:20210617T093000Z DTEND:20210617T101500Z DTSTAMP:20260417T111237Z UID:Oneworldmeeting/3 DESCRIPTION:Title: Effects of rough coasts on the wind-driven oceanic motion\nby Gabriela López Ruiz as part of One world meeting of young mathematicians in fluid dynamics\n\n\nAbstract\nSurface roughness has been identified as an essential parameter in fluid flow since the nineteenth century\, but it s effects on fluid dynamics are not fully understood. This talk regards th e impact of coastal rough topography on oceanic circulation at the mesosca le. We study a singular perturbation problem from meteorology known as the single-layered quasi-geostrophic model. Assuming the rough coasts do not present a particular structure\, the governing boundary layer equations ar e defined in infinite domains with not-decaying boundary data. Additionall y\, the eastern boundary layer exhibits convergence issues far from the bo undary. In this regime\, we establish the well-posedness of the boundary l ayer profiles in Kato spaces by adding ergodicity properties and using pse udo-differential analysis. We construct an approximate solution to the ori ginal problem and show convergence results.\n LOCATION:https://researchseminars.org/talk/Oneworldmeeting/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Roberta Bianchini DTSTART:20210617T123000Z DTEND:20210617T131500Z DTSTAMP:20260417T111237Z UID:Oneworldmeeting/4 DESCRIPTION:Title: Nonlinear inviscid damping and shear-buoyancy instability in the t wo-dimensional Boussinesq equations\nby Roberta Bianchini as part of O ne world meeting of young mathematicians in fluid dynamics\n\n\nAbstract\n In this talk\, we discuss the long-time properties of the two-dimensional inviscid Boussinesq equations near a stably stratified Couette flow\, for a small initial perturbation of size $\\epsilon$ in a suitable Gevrey clas s. Under the classical Miles-Howard stability criterion on the Richardson number\, we show that the system experiences a shear-buoyancy instability: the density variation and velocity undergo an $O(t^{-1/2})$ inviscid damp ing while the vorticity and density gradient grow as $O(t^{1/2})$. The res ult holds at least until the natural\, nonlinear timescale $t \\approx \\v arepsilon^{-2}$. This is a joint work with Jacob Bedrossian\, Michele Coti Zelati and Michele Dolce.\n LOCATION:https://researchseminars.org/talk/Oneworldmeeting/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Chistopher Maulén DTSTART:20210617T131500Z DTEND:20210617T140000Z DTSTAMP:20260417T111237Z UID:Oneworldmeeting/5 DESCRIPTION:Title: Asymptotic stability manifolds for solitons in the generalized Goo d Boussinesq equation\nby Chistopher Maulén as part of One world meet ing of young mathematicians in fluid dynamics\n\n\nAbstract\nIn this talk\ , I shall consider the generalized Good-Boussinesq model in one dimension\ , with power nonlinearity and data in the energy space $H^1\\times L^2$.I will present in more detail the long-time behavior of zero-speed solitary waves\, or standing waves. By using virial identities\, in the spirit of K owalczyk\, Martel\, and Muñoz\, we construct and characterize a manifold of even-odd initial data around the standing wave for which there is asymp totic stability in the energy space.\n LOCATION:https://researchseminars.org/talk/Oneworldmeeting/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Neel Patel DTSTART:20210617T143000Z DTEND:20210617T151500Z DTSTAMP:20260417T111237Z UID:Oneworldmeeting/6 DESCRIPTION:Title: Blow-Up for SQG Patches\nby Neel Patel as part of One world me eting of young mathematicians in fluid dynamics\n\n\nAbstract\nThe two-dim ensional surface quasi-geostrophic (SQG) equation is a model for atmospher ic or oceanic flows and has strong structural similarity with the 3D Euler equation. Patch solutions represent sharp temperature fronts for the 2D S QG equation\, similar to vortex patches for 2D Euler. Interpolating betwee n the 2D Euler equation and the 2D SQG equation\, one obtains the one-para meter 0≤ alpha ≤1 family of generalized SQG equations. We will discuss a class of patch solutions that become singular in finite time for a subf amily of these equations in the half-space setting as well as blow-up crit eria and well-posedness for patches in the full-space.\n LOCATION:https://researchseminars.org/talk/Oneworldmeeting/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Annalaura Stingo DTSTART:20210617T151500Z DTEND:20210617T160000Z DTSTAMP:20260417T111237Z UID:Oneworldmeeting/7 DESCRIPTION:Title: Almost-global well-posedness for 2d strongly-coupled wave-Klein-Go rdon systems\nby Annalaura Stingo as part of One world meeting of youn g mathematicians in fluid dynamics\n\n\nAbstract\nIn this talk we discuss the almost-global well-posedness of a wide class of coupled Wave-Klein-Gor don equations in 2+1 space-time dimensions\, when initial data are small a nd localized. The Wave-Klein-Gordon systems arise from several physical mo dels especially related to General Relativity but few results are known at present in lower space-time dimensions. Compared with prior related resul ts\, we here consider strong quadratic quasilinear couplings between the w ave and the Klein-Gordon equation and no restriction is made on the suppor t of the initial data which are supposed to only have a mild decay at infi nity and very limited regularity. Our proof relies on a combination of ene rgy estimates localized to dyadic space-time regions and pointwise interpo lation type estimates within the same regions. This is a joint work with M . Ifrim.\n LOCATION:https://researchseminars.org/talk/Oneworldmeeting/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Pei Su DTSTART:20210618T073000Z DTEND:20210618T081500Z DTSTAMP:20260417T111237Z UID:Oneworldmeeting/8 DESCRIPTION:Title: Boundary control problem of the water waves system in a tank\n by Pei Su as part of One world meeting of young mathematicians in fluid dy namics\n\n\nAbstract\nHere we are interested in the boundary control probl em of the small-amplitude water waves system in a rectangular tank. The mo del actually we used here is a fully linear and fully dispersive approxima tion of Zakharov-Craig-Sulem formulation constrained in a rectangle\, in p articular\, with a wave maker. The wave maker acts on one lateral boundary \, by imposing the acceleration of the fluid in the horizontal direction\, as a scalar input signal. Firstly\, we introduce the Dirichlet to Neumann and Neumann to Neumann maps\, asscociated to the certain edges of the dom ain\, so that the system reduces to a well-posed linear control system. Th en we consider the stabilizability issue on the gravity and gravity-capill ary waves. It turns out that\, in both cases\, there exists a feedback fun ctional\, such that the corresponding control system is strongly stable. F inally\, we consider the asymptotic behaviour of the above system in shall ow water regime\, i.e. the horizontal scale of the domain is much larger t han the typical water depth. We prove that the solution of the water waves system converges to the solution of the one dimensional wave equation wit h Neumann boundary control\, when taking the shallowness limit. Our approa ch is based on a detailed analysis of the Fourier series and the dimension less version of the evolution operators mentioned above\, as well as a sca ttering semigroup and the Trotter-Kato approximation theorem. This is a jo int work with M. Tucsnak (Bordeaux) and G. Weiss (Tel Aviv).\n LOCATION:https://researchseminars.org/talk/Oneworldmeeting/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Kai Koike DTSTART:20210618T081500Z DTEND:20210618T090000Z DTSTAMP:20260417T111237Z UID:Oneworldmeeting/9 DESCRIPTION:Title: Refined pointwise estimates for 1D viscous compressible flows with application to long-time behavior of a point mass\nby Kai Koike as pa rt of One world meeting of young mathematicians in fluid dynamics\n\n\nAbs tract\nThink of a point mass moving through a 1D viscous compressible flui d. It's not difficult to imagine that its velocity $V(t)$ would somehow de cay to zero as time $t$ goes to infinity. In fact\, numerical experiments suggest that it actually decays as $V(t)\\sim t^{-3/2}$. In one of my prev ious works (https://www.sciencedirect.com/science/article/abs/pii/S0022039 620304666)\, I showed an upper bound of the type $V(t)=O(t^{-3/2})$. Howev er\, it remained to be answered whether this decay estimate is optimal or not\, that is\, whether we can prove a corresponding lower bound of the fo rm $C^{-1}t^{-3/2}\\leq |V(t)|$. Concerning this problem\, I recently obta ined a simple necessary and sufficient condition (on the initial data) for the bound $C^{-1}t^{-3/2}\\leq |V(t)|$ to hold (https://arxiv.org/abs/201 0.06578)\, hence answering the question of optimality. This result is a co rollary to refined pointwise decay estimates of solutions obtained through a very detailed analysis using Green's functions techniques. I shall expl ain these more in detail in the talk.\n LOCATION:https://researchseminars.org/talk/Oneworldmeeting/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefano Scrobogna DTSTART:20210618T093000Z DTEND:20210618T101500Z DTSTAMP:20260417T111237Z UID:Oneworldmeeting/10 DESCRIPTION:Title: On the effect of viscosity in surface gravity waves\nby Stefa no Scrobogna as part of One world meeting of young mathematicians in fluid dynamics\n\n\nAbstract\nThe motion of water waves is a classical research topic that has attracted a lot of attention from many different researche rs in Mathematics\, Physics and Engineering and it is classically modeled by the free-boudary irrotational Euler equations. Usually\, these assumpti ons are enough to describe the main part of the dynamics of real water wav es\, however\, discrepancies between experimental experiences and computer simulations show that sometimes viscosity needs to be taken into account. In this setting the Euler equations should be replaced by the Navier-Stok es equations and the irrotationality hypothesis has to be dropped. It is k nown however\, since the works of Boussinesq (1895) and Lamb (1932) that t he vorticity plays a role only close to the free boundary\, thus\, it woul d be desirable to add dissipative effects to the water waves equations wit hout going all the way to the Navier-Stokes equations and the subsequent r emoval of the irrotationality assumption. This problem has been addressed by a number of people starting with Boussinesq and Lamb\, in this talk we will investigate a a model proposed by Dias\, Dyachenko & Zakharov (Physic s Letters A 2008). Joint work with R. Granero-Belinchón.\n LOCATION:https://researchseminars.org/talk/Oneworldmeeting/10/ END:VEVENT END:VCALENDAR