The Global Well-Posedness for the Compressible Fluid Model of Korteweg Type
Miho Murata, Yoshihiro Shibata
Abstract
In this paper, we consider the compressible fluid model of Korteweg type which can be used as a phase transition model. It is shown that the system admits a unique, global strong solution for small initial data in ${\Bbb R}^N$, $3\leq N \leq 7$. In this study, the main tools are the maximal $L_p$-$L_q$ regularity and $L_p$-$L_q$ decay properties of solutions to the linearized equations.
Topics & Concepts
MathematicsCompressibilityType (biology)Mathematical analysisCompressible flowKorteweg–de Vries equationPhase transitionMathematical physicsApplied mathematicsPhysicsThermodynamicsNonlinear systemGeologyQuantum mechanicsPaleontologyNavier-Stokes equation solutionsAdvanced Mathematical Physics ProblemsGeometric Analysis and Curvature Flows