In this paper, we examine the classical solvability of the Cauchy problem for a pseudoparabolic equation with initial functions from the class \(\mathbb {C}^{2+\alpha }(\mathbb {R}^3)\) , where \(\alpha \in (0,1)\) . For this type of the initial functions, we prove the existence of a unique classical solution of the Cauchy problem in the class \(\mathbb {C}^{(1)}([0,T];\mathbb {C}^{\alpha }(1+|x|^2)^{3/8};\mathbb {R}^3))\) for each \(T \in (0,T_0)\) , where either \(T_0=+\infty \) or \(T_0<+\infty \) is the blow-up time. The proof of the solvability of the Cauchy problem is based on the properties of the corresponding volume potential in Hölder spaces.
