论文标题
同质besov空间中非抗性的MHD方程的寿命和本地适合度的估计值
The estimate of lifespan and local well-posedness for the non-resistive MHD equations in homogeneous Besov spaces
论文作者
论文摘要
在本文中，我们主要研究了非抗性MHD方程的库奇问题。我们首先在同质的besov空间中建立局部存在$ \ dot {b}^{\ frac {d} {p} {p} -1} _ {p，1} \ times \ dot \ dot {b}^{\ frac {\ frac {d} {d} {d} {p}} {取决于初始数据的Littlewood-Paley分解的规范的解决方案。然后，我们证明，如果初始数据$（u^n_0，b^n_0）\ rightarrow（u_0，b_0）$ in $ \ dot {b}^{b}^{\ frac {d} {d} {p} {p} -1} _ { \ dot {b}^{\ frac {d} {p}} _ {p，1} $，然后，相应的存在时间$ t_n \ rightarrow t $，这意味着它们具有寿命的常见下限。最后，我们证明，当$ p \ leq 2d $时，数据之间的分解图不断取决于初始数据。因此，在哈玛德意义上，非耐药性MHD方程是均匀的BESOV空间中的局部良好性。我们获得的结果大大提高了\ cite {li1，chemin1，feffer2}的最新结果。
In this paper, we mainly investigate the Cauchy problem of the non-resistive MHD equation. We first establish the local existence in the homogeneous Besov space $\dot{B}^{\frac{d}{p}-1}_{p,1}\times \dot{B}^{\frac{d}{p}}_{p,1}$ with $p<\infty$, and give a lifespan $T$ of the solution which depends on the norm of the Littlewood-Paley decomposition of the initial data. Then, we prove that if the initial data $(u^n_0,b^n_0)\rightarrow (u_0,b_0)$ in $\dot{B}^{\frac{d}{p}-1}_{p,1}\times \dot{B}^{\frac{d}{p}}_{p,1}$, then the corresponding existence times $T_n\rightarrow T$, which implies that they have a common lower bound of the lifespan. Finally, we prove that the data-to-solutions map depends continuously on the initial data when $p\leq 2d$. Therefore the non-resistive MHD equation is local well-posedness in the homogeneous Besov space in the Hadamard sense. Our obtained result improves considerably the recent results in \cite{Li1,chemin1,Feffer2}.
