O problema de Cauchy para o sistema de Liu-Kubota-Ko

AUTOR(ES)
DATA DE PUBLICAÇÃO

2002

RESUMO

ln this work we consider the initial value problem for the Liu-Kubota-Ko system {Ut + auux - 1 1 (MHl) Ux - /2 (MH2) UX + /2 (NH2) VX = O Vt + bvvx -/3 (MH3) Vx -/4 (.1 vfH2) Vx + /4 (NHJ Ux = O u (x, O) - Uo E H:, s >J v (x, O) - Vo E H , s >"2 (LKK) where the symbol of the operator NH2 is n(k) = sinh_H2 and the symbol of the operator MHi is mi(k) = kcoth(kHi) - Jii o The above system is a physical model for waves in laboratory studies and in certain regime in oceans and lakeso ln natural environments, various effects conspire to produce water basins having density variations with regard to deptho Often these variations consist of rather thin regions of substantial variation concatenated with larger regions of essentially homogeneous fluido ln this situation a region of sharp variation is named a pycnocline. A more complex situation is such that the underlying stratification features two pyc noclines. ln the case the pycnoclines are relatively far apart, but not so distant that motion on one is decoupled from the other, Liu, Kubota &Ko have derived the above model consisting of a coupled pair of intermediate long wave-type equationso. ln [ABS], this system was treated mainly from the point of view of solitary waveso ln this work we use Kato s theory (see [Kl] and [K4]) for quasi linear evolution equation to show the local well-posedness of the initial value problem associated to the LKK system in the Sobolev space HS(IR) x HS(IR) for s >_

ASSUNTO(S)

cauchy semigrupos de operadores equações diferenciais parciais problemas de

ACESSO AO ARTIGO

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