In this paper,the asymptotics of the solution of the initial boundary value problem for a sixth-order nonlinear partial differential equation of Boussinesq type is studied.First,the energy function is obtained.Then,ap...In this paper,the asymptotics of the solution of the initial boundary value problem for a sixth-order nonlinear partial differential equation of Boussinesq type is studied.First,the energy function is obtained.Then,apriori evaluations for this function are obtained.Then,by imposing some conditions on the function on the right-hand side of the equation and using appropriate inequalities,it is shown that the solution is asymptotically damped.展开更多
In this paper,we study the subcritical dissipative quasi-geostrophic equa-tion.By using the Littlewood Paley theory,Fourier analysis and standard techniques we prove that there exists a unique global-in-time solution ...In this paper,we study the subcritical dissipative quasi-geostrophic equa-tion.By using the Littlewood Paley theory,Fourier analysis and standard techniques we prove that there exists a unique global-in-time solution for small initial data belonging to the critical Fourier-Besov-Morrey spaces FN^(3-2a+(λ-2)/p)_(p,λ,q).Moreover,we show the asymptotic behavior of the global solution v.i.e.||v(t)||FN^(3-2a+(λ-2)/p)_(p,λ,q)decays to zero as time goes to infinity.展开更多
文摘In this paper,the asymptotics of the solution of the initial boundary value problem for a sixth-order nonlinear partial differential equation of Boussinesq type is studied.First,the energy function is obtained.Then,apriori evaluations for this function are obtained.Then,by imposing some conditions on the function on the right-hand side of the equation and using appropriate inequalities,it is shown that the solution is asymptotically damped.
文摘In this paper,we study the subcritical dissipative quasi-geostrophic equa-tion.By using the Littlewood Paley theory,Fourier analysis and standard techniques we prove that there exists a unique global-in-time solution for small initial data belonging to the critical Fourier-Besov-Morrey spaces FN^(3-2a+(λ-2)/p)_(p,λ,q).Moreover,we show the asymptotic behavior of the global solution v.i.e.||v(t)||FN^(3-2a+(λ-2)/p)_(p,λ,q)decays to zero as time goes to infinity.
