Optimal Lp–Lq convergence rates for the compressible Navier–Stokes equations with potential force
Optimal Lp–Lq convergence rates for the compressible Navier–Stokes equations with potential force
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DOI：
10.1016/j.jde.2007.03.008
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发表时间：
2007-07
影响因子：
2.4
通讯作者：
Renjun Duan;Hongxia Liu;S. Ukai;Tong Yang
中科院分区：
文献类型：
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作者：
Renjun Duan;Hongxia Liu;S. Ukai;Tong Yang
在这篇文章中，我们讨论了在整个空间中具有潜在外力的可压缩Navier-Stokes方程的最优Lp-Lq收敛速度。在某些Sobolev空间中，在初始摄动和外力均为小的假设下，得到了当初始摄动在LpWith 1⩽p<；6/5中有界时，解的Lq范数为2⩽q⩽6及其一阶导数在L2范数下的最优收敛速度.证明是基于非线性问题解的能量估计和相应线性化算子生成的半群上的一些Lp-Lq估计.
In this paper, we are concerned with the optimal Lp–Lqconvergence rates for the compressible Navier–Stokes equations with a potential external force in the whole space. Under the smallness assumption on both the initial perturbation and the external force in some Sobolev spaces, the optimal convergence rates of the solution in Lq-norm with 2⩽q⩽6 and its first order derivative in L2-norm are obtained when the initial perturbation is bounded in Lpwith 1⩽p<6/5. The proof is based on the energy estimates on the solution to the nonlinear problem and some Lp–Lqestimates on the semigroup generated by the corresponding linearized operator.