Local wellposedness of the modified KP-I equations in periodic setting with small initial data

2019/11/20 by Francisc Bozgan, Bozgan, Francisc
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1911.09767

Abstract

We prove local well-posedness of partially periodic and periodic modified KP-I equations, namely for ∂_t u+(-1)^(l+1)/(2)∂^l_x u-∂_x^-1∂_y² u+u²∂_x u=0 in the anisotropic Sobolev space H^s,s(ℝ× \mathbbT) if l=3 and s>2, in H^s,s(\mathbbT× \mathbbT) if l=3 and s>(19)/(8), and in H^s,s(ℝ× \mathbbT) if l=5 and s>(5)/(2). All three results require the initial data to be small.

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