TY - JOUR

T1 - On the well-posedness of a mathematical model describing water-mud interaction

AU - Escher, Joachim

AU - Matioc, Anca Voichita

PY - 2012/9/14

Y1 - 2012/9/14

N2 - In this paper, we consider a mathematical model describing the two-phase interaction between water and mud in a water canal when the width of the canal is small compared with its depth. The mud is treated as a non-Newtonian fluid, and the interface between the mud and fluid is allowed to move under the influence of gravity and surface tension. We reduce the mathematical formulation, for small boundary and initial data, to a fully nonlocal and nonlinear problem and prove its local well-posedness by using abstract parabolic theory.

AB - In this paper, we consider a mathematical model describing the two-phase interaction between water and mud in a water canal when the width of the canal is small compared with its depth. The mud is treated as a non-Newtonian fluid, and the interface between the mud and fluid is allowed to move under the influence of gravity and surface tension. We reduce the mathematical formulation, for small boundary and initial data, to a fully nonlocal and nonlinear problem and prove its local well-posedness by using abstract parabolic theory.

KW - classical solution

KW - non-Newtonian fluid

KW - two-phase moving boundary problem

UR - http://www.scopus.com/inward/record.url?scp=84879412896&partnerID=8YFLogxK

U2 - 10.1002/mma.2692

DO - 10.1002/mma.2692

M3 - Article

AN - SCOPUS:84879412896

VL - 36

SP - 1388

EP - 1398

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 11

ER -