We consider a generalization of the Boussinesq equation obtained by adding a term of the form a(t,x,u)∂3xu . We prove local in time well-posedness of the Cauchy problem in Sobolev spaces under a suitable decay condition on the real part of the coefficient a(t,x,u), as x→∞.
Well-posedness for a generalized boussinesq equation
ASCANELLI, Alessia
;BOITI, Chiara
2015
Abstract
We consider a generalization of the Boussinesq equation obtained by adding a term of the form a(t,x,u)∂3xu . We prove local in time well-posedness of the Cauchy problem in Sobolev spaces under a suitable decay condition on the real part of the coefficient a(t,x,u), as x→∞.File in questo prodotto:
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