Landau-Lifshitz-Bloch equation on Riemannian manifold
In this article, we bring in Landau-Lifshitz-Bloch(LLB) equation on $m$-dimensional closed Riemannian manifold and prove that it admits a unique local solution. In addition, if $m\geqslant3$ and $L^{\infty}-$norm of initial data is sufficiently small, the solution can be extended globally. Moreover,...
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| creator | Guo, Boling Jia, Zonglin |
| description | In this article, we bring in Landau-Lifshitz-Bloch(LLB) equation on
$m$-dimensional closed Riemannian manifold and prove that it admits a unique
local solution. In addition, if $m\geqslant3$ and $L^{\infty}-$norm of initial
data is sufficiently small, the solution can be extended globally. Moreover, if
$m=2$, we can prove that the unique solution is global without assuming small
initial data. |
| doi_str_mv | 10.48550/arxiv.1807.00989 |
| format | Article |
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$m$-dimensional closed Riemannian manifold and prove that it admits a unique
local solution. In addition, if $m\geqslant3$ and $L^{\infty}-$norm of initial
data is sufficiently small, the solution can be extended globally. Moreover, if
$m=2$, we can prove that the unique solution is global without assuming small
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$m$-dimensional closed Riemannian manifold and prove that it admits a unique
local solution. In addition, if $m\geqslant3$ and $L^{\infty}-$norm of initial
data is sufficiently small, the solution can be extended globally. Moreover, if
$m=2$, we can prove that the unique solution is global without assuming small
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$m$-dimensional closed Riemannian manifold and prove that it admits a unique
local solution. In addition, if $m\geqslant3$ and $L^{\infty}-$norm of initial
data is sufficiently small, the solution can be extended globally. Moreover, if
$m=2$, we can prove that the unique solution is global without assuming small
initial data.</abstract><doi>10.48550/arxiv.1807.00989</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Analysis of PDEs |
| title | Landau-Lifshitz-Bloch equation on Riemannian manifold |
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