TY - JOUR
T1 - Interaction Equations for Short and Long Dispersive Waves
AU - Bekiranov, Daniella
AU - Ogawa, Takayoshi
AU - Ponce, Gustavo
N1 - Funding Information:
The work of T. Ogawa is partially supported by UC Santa Barbara, The Sumitomo Foundation, and Japan ministry of Education, Science and Culture. The work of G. Ponce is partially supported by NSF grant.
PY - 1998/10/1
Y1 - 1998/10/1
N2 - We show the time-local well-posedness for a system of nonlinear dispersive equations for the water wave interaction[formula]It is shown that for any initial data (u0,v0)∈Hs(R)×Hs-1/2(R) (s≥0), the solution for the above equation uniquely exists in a subset ofC((-T,T);Hs)×C((-T,T);Hs-1/2) and depends continuously on the data. By virtue of a special structure of the nonlinear coupling, the solution is stable under a singular limiting process.
AB - We show the time-local well-posedness for a system of nonlinear dispersive equations for the water wave interaction[formula]It is shown that for any initial data (u0,v0)∈Hs(R)×Hs-1/2(R) (s≥0), the solution for the above equation uniquely exists in a subset ofC((-T,T);Hs)×C((-T,T);Hs-1/2) and depends continuously on the data. By virtue of a special structure of the nonlinear coupling, the solution is stable under a singular limiting process.
UR - http://www.scopus.com/inward/record.url?scp=0001306532&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0001306532&partnerID=8YFLogxK
U2 - 10.1006/jfan.1998.3257
DO - 10.1006/jfan.1998.3257
M3 - Article
AN - SCOPUS:0001306532
VL - 158
SP - 357
EP - 388
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 2
ER -