Existence of R‐bounded solution operator families for a compressible fluid model of Korteweg type on the half‐space

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  • Hirokazu Saito
    Department of Mathematics The University of Electro‐Communications 5‐1 Chofugaoka 1‐chome Chofu 182‐8585 Tokyo Japan

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<jats:p>The aim of this paper is to show the existence of ‐bounded solution operator families for a generalized resolvent problem on the half‐space arising from a compressible fluid model of Korteweg type. Our main result covers not only the large resolvent parameter so that <jats:styled-content>|<jats:italic>λ</jats:italic>|≥<jats:italic>δ</jats:italic></jats:styled-content> for some <jats:styled-content><jats:italic>δ</jats:italic> > 0</jats:styled-content>, but also small <jats:styled-content><jats:italic>λ</jats:italic></jats:styled-content> satisfying <jats:styled-content>|<jats:italic>λ</jats:italic>|≤<jats:italic>δ</jats:italic></jats:styled-content>.</jats:p>

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