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Local well-posedness for the KdV hierarchy at high regularity
Carlos E. Kenig,Didier Pilod +1 more
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In this article, the authors prove well-posedness in Sobolev spaces with high regularity for a class of nonlinear higher-order dispersive equations generalizing the KdV hierarchy both on the line and on the torus.Abstract:
We prove well-posedness in $L^2$-based Sobolev spaces $H^s$ at high regularity for a class of nonlinear higher-order dispersive equations generalizing the KdV hierarchy both on the line and on the torus.read more
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On the local well-posedness for a full-dispersion Boussinesq system with surface tension
Henrik Kalisch,Didier Pilod +1 more
TL;DR: In this paper, the authors prove local-in-time well-posedness for a fully dispersive Boussinesq system arising in the context of free surface water waves in two and three spatial dimensions.
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Low regularity Cauchy problem for the fifth-order modified KdV equations on $\mathbb{T}$
TL;DR: In this paper, the authors considered the fifth-order modified Korteweg-de Vries (modified KdV) equation under the periodic boundary condition and proved the local well-posedness in $H^s(mathbb T)$s > 2.
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The Flow of Polynomial Roots Under Differentiation
TL;DR: In this article, a nonlocal nonlinear partial differential equation was derived by Stefan Steinerberger to model dynamics of roots of polynomials under differentiation, and the same equation has also been recently obtained formally by Dimitri Shlyakhtenko and Terence Tao as the evolution equation for free fractional convolution of a measure -an object in free probability that is also related to minor processes for random matrices.
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On the local well-posedness for a full dispersion Boussinesq system with surface tension
Henrik Kalisch,Didier Pilod +1 more
TL;DR: In this article, the authors prove local-in-time well-posedness for a fully dispersive Boussinesq system arising in the context of free surface water waves in two and three spatial dimensions.
Journal ArticleDOI
Well-Posedness for a Whitham-Boussinesq System with Surface Tension
TL;DR: In this article, the Cauchy problem for a particular Whitham-Boussinesq system modelling surface waves of an inviscid incompressible fluid layer was considered.