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Optimal decay rates and small global solutions to the dissipative Boussinesq equation
Author(s) -
Su Xiao,
Wang Shubin
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5843
Subject(s) - mathematics , pointwise , dissipative system , uniqueness , norm (philosophy) , initial value problem , mathematical analysis , fourier transform , work (physics) , space (punctuation) , physics , thermodynamics , linguistics , philosophy , quantum mechanics , political science , law
This work is devoted to the small amplitude solutions for the initial value problem of the multidimensional dissipative Boussinesq equation. We firstly derive the pointwise estimates of the fundamental solutions by the energy method in the Fourier space. We give the asymptotic profiles of solutions to the corresponding linear problem to get the optimal decay rate for theH ̇ s ‐norm of solutions in all space dimensions. Under smallness assumptions on the initial data, we study the global existence and uniqueness of solutions by the contractive mapping principle in the solution spaces with time weighted norm.