<p>In this article, we investigate the continuation of strong solutions to the incompressible Navier-Stokes equations, focusing on the behavior of the middle eigenvalue of the strain tensor within the framework of Vishik spaces. In particular, we establish sharp continuation criteria in the spaces <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^2(0,T; \dot{V}^{-1}_{\infty ,\infty ,2}(\mathbb {R}^3))\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mn>2</mn> </msup> <mrow> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mi>T</mi> <mo>;</mo> <msubsup> <mover accent="true"> <mi>V</mi> <mo>˙</mo> </mover> <mrow> <mi>∞</mi> <mo>,</mo> <mi>∞</mi> <mo>,</mo> <mn>2</mn> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>3</mn> </msup> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L^1(0,T; \dot{V}^{0}_{\infty ,\infty ,1}(\mathbb {R}^3))\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mn>1</mn> </msup> <mrow> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mi>T</mi> <mo>;</mo> <msubsup> <mover accent="true"> <mi>V</mi> <mo>˙</mo> </mover> <mrow> <mi>∞</mi> <mo>,</mo> <mi>∞</mi> <mo>,</mo> <mn>1</mn> </mrow> <mn>0</mn> </msubsup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>3</mn> </msup> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, providing a positive resolution to an open problem related to the global regularity of the Navier-Stokes equations.</p>