On Exponential Splitting Methods for Semilinear Abstract Cauchy problems

Abstract Due to the seminal works of Hochbruck and Ostermann (Appl Numer Math 53(2–4):323–339, 2005, Acta 19:209–286, 2010) exponential splittings are well established numerical methods utilizing operator semigroup theory for treatment semilinear evolution equations whose principal linear part involves a sectorial with angle greater than $$\frac{\pi }{2}$$ π 2 (meaning essentially holomorphy underlying semigroup). The present paper contributes this subject by relaxing sectoriality condition, but in turn requiring that operators act consistently on an interpolation couple (or scale Banach spaces). Our conditions (on semilinearity) inspired approach Kato (Math Z 187(4):471–480, 1984) local solvability Navier–Stokes equation, where $$\textrm{L}^p$$ L p - $$\textrm{L}^r$$ r -smoothing Stokes was fundamental. abstract theoretic result is applicable latter problem (as already Ostermann), or more generally setting (2005), also allows consideration examples, such as non-analytic Ornstein–Uhlenbeck semigroups flow around rotating bodies.