Strong solutions of 3D compressible Oldroyd‐B fluids. (1st October 2012)

• Record Type: Journal Article
• Authors: Fang, Daoyuan; Zi, Ruizhao
• Is Part Of: Mathematical methods in the applied sciences. Volume 36:Number 11(2013:Jul. 30)
• Page Start: 1423
• Page End: 1439
• Publication Date: 2012-10-01
• Subjects: Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.2695
• Languages: English
• ISSNs: 0170-4214

Abstract

<abstract abstract-type="main" id="mma2695-abs-0001"> <title> <x xml:space="preserve">Abstract</x> </title> <p id="mma2695-para-0001">This paper is concerned with a compressible viscoelastic fluids of Oldroyd‐B type. We prove the existence of unique local strong solutions for all initial data satisfying some compatibility condition. Moreover, we establish a blow‐up criterion for the strong solution in terms of the <inline-graphic mimetype="image" xlink:href="ark:/27927/pgg22frx67p" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="block" altimg="urn:x-wiley:01704214:media:mma2695:mma2695-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>L</mml:mi><mml:mi>t</mml:mi><mml:mo class="MathClass-rel">∞</mml:mo></mml:msubsup><mml:msubsup><mml:mi>L</mml:mi><mml:mi>x</mml:mi><mml:mo class="MathClass-rel">∞</mml:mo></mml:msubsup></mml:math> norm of the density tensor <italic>ρ</italic> and the <inline-graphic mimetype="image" xlink:href="ark:/27927/pgg22frx62x" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="block" altimg="urn:x-wiley:01704214:media:mma2695:mma2695-math-0002" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>L</mml:mi><mml:mi>t</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:msubsup><mml:mi>L</mml:mi><mml:mi>x</mml:mi><mml:mo class="MathClass-rel">∞</mml:mo></mml:msubsup></mml:math> norm of the symmetric tensor of constraints <italic>τ</italic>. All the results hold for the initial density vanishing from below. Copyright © 2012 John Wiley & Sons, Ltd.</p> </abstract>