In this paper, we study a free boundary problem for the 1D viscous radiative and reactive gas. We prove that for any large initial data, the problem admits a unique global generalized solution. Meanwhile, we obtain th...In this paper, we study a free boundary problem for the 1D viscous radiative and reactive gas. We prove that for any large initial data, the problem admits a unique global generalized solution. Meanwhile, we obtain the time-asymptotic behavior of the global solutions. Our results improve and generalize the previous work.展开更多
In this paper, we investigate the existence of time-periodic solutions to the n-dimension hydrodynamic model for a reacting mixture with a time-periodic external force when the dimension is under some smallness assump...In this paper, we investigate the existence of time-periodic solutions to the n-dimension hydrodynamic model for a reacting mixture with a time-periodic external force when the dimension is under some smallness assumption. The energy method combined with the spectral analysis is used to obtain the optimal decay estimates on the linearized solution operator. We study the existence and uniqueness of the time-periodic solution in some suitable function space by using a fixed point method and the decay estimates. Furthermore, we obtain the time asymptotic stability of the time-periodic solution.展开更多
We consider the full compressible Navier-Stokes equations with reaction diffusion.A global existence and uniqueness result of the strong solution is established for the Cauchy problem when the initial data is in a nei...We consider the full compressible Navier-Stokes equations with reaction diffusion.A global existence and uniqueness result of the strong solution is established for the Cauchy problem when the initial data is in a neighborhood of a trivially stationary solution.The appearance of the difference between energy gained and energy lost due to the reaction is a new feature for the flow and brings new difficulties.To handle these,we construct a new linearized system in terms of a combination of the solutions.Moreover,some optimal timedecay estimates of the solutions are derived when the initial perturbation is additionally bounded in L1.It is worth noticing that there is no decay loss for the highest-order spatial derivatives of the solution so that the long time behavior for the hyperbolic-parabolic system is exactly the same as that for the heat equation.As a byproduct,the above time-decay estimate at the highest order is also valid for compressible Navier-Stokes equations.The proof is accomplished by virtue of Fourier theory and a new observation for cancellation of a low-medium-frequency quantity.展开更多
基金Supported by the NNSF of China(Grant No.11671367)the Natural Science Foundation of He’nan Province(Grant No.152300410227)the Key Research Projects of He’nan Higher Education Institutions(Grant No.18A110038)
文摘In this paper, we study a free boundary problem for the 1D viscous radiative and reactive gas. We prove that for any large initial data, the problem admits a unique global generalized solution. Meanwhile, we obtain the time-asymptotic behavior of the global solutions. Our results improve and generalize the previous work.
文摘In this paper, we investigate the existence of time-periodic solutions to the n-dimension hydrodynamic model for a reacting mixture with a time-periodic external force when the dimension is under some smallness assumption. The energy method combined with the spectral analysis is used to obtain the optimal decay estimates on the linearized solution operator. We study the existence and uniqueness of the time-periodic solution in some suitable function space by using a fixed point method and the decay estimates. Furthermore, we obtain the time asymptotic stability of the time-periodic solution.
基金supported by National Natural Science Foundation of China(Grant Nos.11871341 and 11571231)supported by National Natural Science Foundation of China(Grant Nos.11671150 and 11722104)。
文摘We consider the full compressible Navier-Stokes equations with reaction diffusion.A global existence and uniqueness result of the strong solution is established for the Cauchy problem when the initial data is in a neighborhood of a trivially stationary solution.The appearance of the difference between energy gained and energy lost due to the reaction is a new feature for the flow and brings new difficulties.To handle these,we construct a new linearized system in terms of a combination of the solutions.Moreover,some optimal timedecay estimates of the solutions are derived when the initial perturbation is additionally bounded in L1.It is worth noticing that there is no decay loss for the highest-order spatial derivatives of the solution so that the long time behavior for the hyperbolic-parabolic system is exactly the same as that for the heat equation.As a byproduct,the above time-decay estimate at the highest order is also valid for compressible Navier-Stokes equations.The proof is accomplished by virtue of Fourier theory and a new observation for cancellation of a low-medium-frequency quantity.
