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In this work, we study the Cauchy problem of the Elastic Beam equation withinitial value in weighted Sobolev space $H^{1,1}(\mathbb{R})$ via the$\bar{\partial}$-steepset descent method. Begin with the Lax pair of theElastic Beam equation, we successfully derive the basic Riemann-Hilbertproblem, which can be used to represent the solutions of the Elastic Beamequation. Then, considering the solitonless region and using the$\bar{\partial}$-steepset descent method, we analyse the long-time asymptoticbehaviors of the solutions for the Elastic Beam equation.

Long-time asymptotics for the Elastic Beam equation in the solitonless region via $\bar{\partial}$ methods