Abstract
AbstractWe consider the SQG equation with dissipation given by a fractional Laplacian of order $$\alpha <\frac{1}{2}$$
α
<
1
2
. We introduce a notion of suitable weak solution, which exists for every $$L^2$$
L
2
initial datum, and we prove that for such solution the singular set is contained in a compact set in spacetime of Hausdorff dimension at most $$\frac{1}{2\alpha } \left( \frac{1+\alpha }{\alpha } (1-2\alpha ) + 2\right) $$
1
2
α
1
+
α
α
(
1
-
2
α
)
+
2
.
Funder
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
National Science Foundation
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Geometry and Topology,General Physics and Astronomy,Mathematical Physics,Analysis
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