Local well-posedness for the sixth-order Boussinesq equation
Copyright policy )Local well-posedness for the sixth-order Boussinesq equation
This work studies the local well-posedness of the initial-value problem for the nonlinear sixth-order Boussinesq equation $u_{tt}=u_{xx}+βu_{xxxx}+u_{xxxxxx}+(u^2)_{xx}$, where $β=\pm1$. We prove local well-posedness with initial data in non-homogeneous Sobolev spaces $H^s(\R)$ for negative indices of $s \in \R$.
16 pages. Submitted
- Universidade Federal de Minas Gerais Brazil
- UNIVERSIDADE DE SAO PAULO Brazil
- Universidade Federal de Minas Gerais Brazil
- Damghan University Iran (Islamic Republic of)
Water waves, gravity waves; dispersion and scattering, nonlinear interaction, Applied Mathematics, local well-posedness, PDEs in connection with fluid mechanics, one space dimension, Boussinesq equation, Mathematics - Analysis of PDEs, Sobolev spaces, Existence, uniqueness, and regularity theory for incompressible inviscid fluids, FOS: Mathematics, initial value problem, Local well-posedness, Initial value problems for nonlinear higher-order PDEs, Analysis, Analysis of PDEs (math.AP)
Water waves, gravity waves; dispersion and scattering, nonlinear interaction, Applied Mathematics, local well-posedness, PDEs in connection with fluid mechanics, one space dimension, Boussinesq equation, Mathematics - Analysis of PDEs, Sobolev spaces, Existence, uniqueness, and regularity theory for incompressible inviscid fluids, FOS: Mathematics, initial value problem, Local well-posedness, Initial value problems for nonlinear higher-order PDEs, Analysis, Analysis of PDEs (math.AP)
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