<p>The aim of this paper is to investigate a higher upper and lower decay rates for the difference <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$u-{\tilde{u}}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>u</mi> <mo>-</mo> <mover accent="true"> <mi>u</mi> <mo stretchy="false">~</mo> </mover> </mrow> </math></EquationSource> </InlineEquation> where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$u$</EquationSource> <EquationSource Format="MATHML"><math> <mi>u</mi> </math></EquationSource> </InlineEquation> is a strong or classical solution of an incompressible (non-)Newtonian fluid in <InlineEquation ID="IEq3"> <EquationSource Format="TEX">${{\mathbb {R}} }^3$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation> with the initial data <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$u_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>u</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">${\tilde{u}}$</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mi>u</mi> <mo stretchy="false">~</mo> </mover> </math></EquationSource> </InlineEquation> is the strong or classical solution of the same equations with large perturbed initial data <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$W_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>W</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>. The proof is based on energy estimates.</p>

Upper and lower convergence rates for (strong or) classical solutions to the 3D incompressible fluid

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发表日期：

2025年10月18日

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Jae-Myoung Kim

摘要

The aim of this paper is to investigate a higher upper and lower decay rates for the difference $u-{\tilde{u}}$ $u - \tilde{u}$ where $u$ $u$ is a strong or classical solution of an incompressible (non-)Newtonian fluid in ${{\mathbb {R}} }^3$ $R^{3}$ with the initial data $u_0$ $u_{0}$ and ${\tilde{u}}$ $\tilde{u}$ is the strong or classical solution of the same equations with large perturbed initial data $W_0$ $W_{0}$ . The proof is based on energy estimates.