论文标题
Besov空间中Landau-Lifshitz-Bloch方程的强大解决方案
Strong solutions of the Landau-Lifshitz-Bloch equation in Besov space
论文作者
论文摘要
我们专注于三维Landau-lifshitz-bloch方程的存在和唯一性，并补充了Besov Space中的初始数据$ \ dot {b} _ {2,1}^{\ frac {\ frac {3} {3} {2}}} $。利用新的换向器估计，我们为$ \ dot {b} _ {2,1}^{\ frac {\ frac {3} {2}} $中的任何初始数据建立了强大解决方案的本地存在和唯一性。当初始数据在$ \ dot {b} _ {2,1}^{\ frac {\ frac {3} {2}} $中足够小时，我们获得了全局的存在和独特性。此外，我们还建立了对Landau-Lifshitz-Bloch方程的解决方案的爆炸标准，然后我们证明了基于爆破标准的新条件下，在Sobolev空间中，全球强大解决方案的全球存在。
We focus on the existence and uniqueness of the three-dimensional Landau-Lifshitz-Bloch equation supplemented with the initial data in Besov space $\dot{B}_{2,1}^{\frac{3}{2}}$. Utilizing a new commutator estimate, we establish the local existence and uniqueness of strong solutions for any initial data in $\dot{B}_{2,1}^{\frac{3}{2}}$. When the initial data is small enough in $\dot{B}_{2,1}^{\frac{3}{2}}$, we obtain the global existence and uniqueness. Furthermore, we also establish a blow-up criterion of the solution to the Landau-Lifshitz-Bloch equation and then we prove the global existence of strong solutions in Sobolev space under a new condition based on the blow-up criterion.
