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<p>We obtain well-posedness and Schauder estimates for a class of linear, quasi-linear and semi-linear second order partial differential equations. We deduce existence and uniqueness of a global smooth solution of a non-linear and non-local equation that we call “semi” incompressible Navier Stokes equation in <InlineEquation ID="IEq1"> <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>.</p>

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Parabolic bootstrap for some non-linear equations

  • 期刊论文

  • 发表日期：

    2025年8月11日

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  • Igor Honoré

摘要

We obtain well-posedness and Schauder estimates for a class of linear, quasi-linear and semi-linear second order partial differential equations. We deduce existence and uniqueness of a global smooth solution of a non-linear and non-local equation that we call “semi” incompressible Navier Stokes equation in \(\mathbb {R}^3\) R 3 .