TY - JOUR
T1 - Well-posedness and analyticity of solutions for the sixth-order Boussinesq equation
AU - Esfahani, Amin
AU - Tesfahun, Achenef
N1 - Publisher Copyright:
© 2024 World Scientific Publishing Company.
PY - 2024
Y1 - 2024
N2 - In this paper, the sixth-order Boussinesq equation is studied. We extend the local well-posedness theory for this equation with quadratic and cubic nonlinearities to the high dimensional case. In spite of having the "bad"fourth term u in the equation, we derive some dispersive estimates leading to the existence of local solutions which also improves the previous results in the cubic case. In addition, we show persistence of spatial analyticity of solutions for the cubic nonlinearity.
AB - In this paper, the sixth-order Boussinesq equation is studied. We extend the local well-posedness theory for this equation with quadratic and cubic nonlinearities to the high dimensional case. In spite of having the "bad"fourth term u in the equation, we derive some dispersive estimates leading to the existence of local solutions which also improves the previous results in the cubic case. In addition, we show persistence of spatial analyticity of solutions for the cubic nonlinearity.
KW - Boussinesq equation
KW - dispersive estimates
KW - local well-posedness
KW - radius of analyticity of solution
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U2 - 10.1142/S0219199724500056
DO - 10.1142/S0219199724500056
M3 - Article
AN - SCOPUS:85185781453
SN - 0219-1997
JO - Communications in Contemporary Mathematics
JF - Communications in Contemporary Mathematics
M1 - 2450005
ER -