| Summary: | This article studies the stochastic evolution of incompressible non-Newtonian fluids of differential type. More precisely, we consider the equations governing the dynamic of a third grade fluid filling a three-dimensional bounded domain <inline-formula><math display="inline"><semantics><mi mathvariant="script">O</mi></semantics></math></inline-formula>, perturbed by a multiplicative white noise. Taking the initial condition in the Sobolev space <inline-formula><math display="inline"><semantics><mrow><msup><mi>H</mi><mn>2</mn></msup><mrow><mo stretchy="false">(</mo><mi mathvariant="script">O</mi><mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula>, and supplementing the equations with a Navier slip boundary condition, we establish the existence of a global weak stochastic solution with sample paths in <inline-formula><math display="inline"><semantics><mrow><msup><mi>L</mi><mo>∞</mo></msup><mrow><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>;</mo><msup><mi>H</mi><mn>2</mn></msup><mrow><mo stretchy="false">(</mo><mi mathvariant="script">O</mi><mo stretchy="false">)</mo></mrow><mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula>.
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