  The existence of finite time blowup solutions for the two-dimensional
Landau--Lifshitz equation is a long-standing problem, which exists in the
literature at least since 2001 (E, Mathematics Unlimited--2001 and Beyond,
Springer, Berlin, P.410, 2001). A more refined description in the equivariant
class is given in (van den Berg and Williams, European J. Appl. Math., 24(6),
912--948, 2013). In this paper, we consider the blowup dynamics of the
Landau--Lifshitz equation $$ \partial_tu=\mathfrak{a}_1u\times\Delta
u-\mathfrak{a}_2u\times(u\times\Delta u),\quad x\in\mathbb{R}^2, $$ where
$u\in\mathbb{S}^2$, $\mathfrak{a}_1+i\mathfrak{a}_2\in\mathbb{C}$ with
$\mathfrak{a}_2\geq0$ and $\mathfrak{a}_1+\mathfrak{a}_2=1$. We prove the
existence of 1-equivariant Krieger--Schlag--Tataru type blowup solutions near
the lowest energy steady state. More precisely, we prove that for any $\nu>1$,
there exists a 1-equivariant finite-time blowup solution of the form $$
u(x,t)=\phi(\lambda(t)x)+\zeta(x,t),\quad \lambda(t)=t^{-1/2-\nu}, $$ where
$\phi$ is a lowest energy steady state and $\zeta(t)$ is arbitrary small in
$\dot{H}^1\cap\dot{H}^2$. The proof is accomplished by renormalizing the blowup
profile and a perturbative analysis in the spirit of (Krieger, Schlag and
Tataru, Invent. Math., 171(3), 543--615, 2008), (Perelman, Comm. Math. Phys.,
330(1), 69--105, 2014) and (Ortoleva and Perelman, Algebra i Analiz, 25(2),
271--294, 2013).
