On the free boundary problem for the Oldroyd-B Model in the maximal - regularity class

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• 作者：Sri Maryani ; ^{sri.maryani@fuji.waseda.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35Q35 ; 76N10
• 刊名：Nonlinear Analysis
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：141
• 期：Complete
• 页码：109-129
• 全文大小：833 K

文摘

In the present work, we prove the local well-posedness of non-Newtonian compressible viscous barotropic fluid flow of Oldroyd-B type with free surface in a bounded domain of 46X16300438&_mathId=si3.gif&_user=111111111&_pii=S0362546X16300438&_rdoc=1&_issn=0362546X&md5=d9358cfd1ecdb61d5af74727fca7eacb" title="Click to view the MathML source">N$N$-dimensional Euclidean space (46X16300438&_mathId=si4.gif&_user=111111111&_pii=S0362546X16300438&_rdoc=1&_issn=0362546X&md5=03f554084ed3634402d1f888ec08ed31" title="Click to view the MathML source">N≥2$N\ge 2$). The key step is to prove the maximal 46X16300438&_mathId=si1.gif&_user=111111111&_pii=S0362546X16300438&_rdoc=1&_issn=0362546X&md5=6d547f6aa73fcac70b433251c453fe9f" title="Click to view the MathML source">L_p$L_p$–46X16300438&_mathId=si2.gif&_user=111111111&_pii=S0362546X16300438&_rdoc=1&_issn=0362546X&md5=51d02156e2c56d288e62cd727c40ce6e" title="Click to view the MathML source">L_q$L_q$ regularity theorem for the linearized equation with the help of the 46X16300438&_mathId=si7.gif&_user=111111111&_pii=S0362546X16300438&_rdoc=1&_issn=0362546X&md5=a3ee1bf5c3bcfad8fd98147381f2e78f" title="Click to view the MathML source">R$\mathcal{R}$-bounded solution operators for the corresponding resolvent problem and Weis’s operator valued Fourier multiplier theorem.