Well-posedness and analyticity of solutions for the sixth-order Boussinesq equation
Esfahani A. Tesfahun A.
1 March 2025World Scientific
Communications in Contemporary Mathematics
2025#27Issue 2
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 badfourth term Δu 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.
Boussinesq equation , dispersive estimates , local well-posedness , radius of analyticity of solution
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Department of Mathematics, Nazarbayev University, Astana, 010000, Kazakhstan
Department of Mathematics
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