Department of

# Mathematics

Seminar Calendar
for Harmonic Analysis and Differential Equations Seminar events the year of Tuesday, March 13, 2018.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, March 13, 2018

1:00 pm in 347 Altgeld Hall,Tuesday, March 13, 2018

#### Low Regularity Global Existence for the Periodic Zakharov System

###### Erin Compaan (MIT)

Abstract: In this talk, we present a low-regularity global existence result for the periodic Zakharov system. This is a dispersive model for the motion of ionized plasma. Its dynamics have been extensively studied, and existence of solutions is in known for data in the Sobolev space $H^\frac12 \times L^2$. We present a global existence result which holds for even rougher data, in a class of Fourier Lebesgue spaces. It is obtained by combining the high-low decomposition method of Bourgain with an almost-conserved energy result of Kishimoto. Combining these two tools allows us to obtain a low-regularity result which was out of reach of either method alone.