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They discovered that the numerical solution of the discretization becomes unbounded despite the fact that theoretically the solution should remain bounded.
The main difficulties are that: usual Lq Lr estimates for the Stokes flow fail in this case; and the projection operator P L1(Rn+)→L1σ(Rn+) becomes unbounded.
Obviously, becomes unbounded as, at the point.
Thus, the ratio in (22) becomes unbounded, contradicting the proper efficiency of (x^) for (P).
where is a non-negative parameter, and the function becomes unbounded at.
(g t,x)) being singular at 0 means that (g t,x)) becomes unbounded when (xrightarrow0^).
Obviously, ((underline{u}, underline{v})) becomes unbounded as (trightarrow T^) at the point (x=0).
Indeed, if y ( t ) → 0 as t → ∞, then the left-hand side of (15) becomes unbounded which is a contradiction.
If the solution u ( x, t ) becomes unbounded in Φ-measure at time t ∗, then t ∗ ≥ T, (8).
Equation (1.1) is singular at 0, which means that g ( t, x ) becomes unbounded when x → 0 +.
Roughly speaking, system (1.1) is singular at 0 means that f ( t, r ) becomes unbounded when r → 0 +.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com