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Theme for TIFR Centre For Applicable Mathematics, Bangalore

Abstract: In this talk, We discuss the Cauchy problem for Hartree equation with convolution nonlinearity $$F(u)$$=$$(K * |u|$$$$^{2k})$$$$u$$, under a specified condition on potential $$K$$ with Cauchy data in modulation spaces $$M$$$$^{p,q}$$$$(R^n)$$.  We will give an overview of the progress in the last decade and ongoing interest in the context of modulation spaces.