TY - JOUR
T1 - Well-posedness of a highly nonlinear shallow water equation on the circle
AU - Duruk Mutlubas, Nilay
AU - Geyer, Anna
AU - Quirchmayr, Ronald
PY - 2020/8/1
Y1 - 2020/8/1
N2 - We present a comprehensive introduction and overview of a recently derived model equation for waves of large amplitude in the context of shallow water waves and provide a literature review of all the available studies on this equation. Furthermore, we establish a novel result concerning the local well-posedness of the corresponding Cauchy problem for space-periodic solutions with initial data from the Sobolev space Hs on the circle for s>3∕2.
AB - We present a comprehensive introduction and overview of a recently derived model equation for waves of large amplitude in the context of shallow water waves and provide a literature review of all the available studies on this equation. Furthermore, we establish a novel result concerning the local well-posedness of the corresponding Cauchy problem for space-periodic solutions with initial data from the Sobolev space Hs on the circle for s>3∕2.
KW - Cubic nonlinearity
KW - Large amplitude waves
KW - Shallow water equation
KW - Well-posedness
UR - http://www.scopus.com/inward/record.url?scp=85081373421&partnerID=8YFLogxK
U2 - 10.1016/j.na.2020.111849
DO - 10.1016/j.na.2020.111849
M3 - Article
AN - SCOPUS:85081373421
SN - 0362-546X
VL - 197
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
M1 - 111849
ER -